Let him try (but there are a few things he'll have to overcome)
Your player has set a lofty goal for themselves, one which has only been accomplished a handful of times before in known history. But there's certainly nothing wrong with ambition in a Vampire game!
That being said, you mentioned something that got my attention. You said:
I’m dreading when I have to bring an Antediluvian in.
That's certainly understandable. Active Antediluvians are expected to signal Gehenna, the end times. Essentially, this character has a plan that will either end with them as one of the most powerful beings in the world, or with the world's near-total destruction. It's hard to think of how to run such an event in a way that permits anything to happen after it in your game. But it's worth noting that this effort could take a very long time. An entire campaign could be structured around the various difficult barriers this character must overcome to even attempt this act.
With that in mind, let's consider some of the obstacles he'll need to overcome to actually accomplish the theft of an Antediluvian's power. And all of these obstacles will give you ways to delay his ultimate attempt, and create interesting and fun chapters in this story.
Antediluvians are hard to find
Knowledge is power, as they say, and thus some knowledge is only available to the very powerful. If the location of all the Antediluvians was public knowledge, none of them would be safe (sometimes from rival clans, and in some cases from their own clan members). As such, they slumber in secret places, whose locations and defenses are difficult to determine.
What does your character need to do to find them? Perhaps build up a huge network of informants and investigators that span the globe, or develop disciplines that rival the powers of the Tremere, or gain political power at the highest level of vampire society that will give him access to secret guarded lore? Maybe he'll need to do all three! And all of these efforts take time and resources. Developing any or all of these methods can be the backbone of a campaign worth of stories.
Diablerie is reviled
Ok, sure: let's be honest here. Diablerie happens more than vampires would like to admit. Two of the 13 current great clans (or more, depending on whom you believe) are built on the diablerization of Antediluvians, and another is publicly in favor of doing as much diablerie as they possibly can. But amongst most of the Camarilla, the act of diablerie is strictly forbidden, except in cases of a blood-hunt. At least as far as the vampire public is concerned, it is the worst thing a vampire can do.
If this character plans to diablerize an Antediluvian, they will need to keep their efforts to do so a secret. That means that any resources they gather towards this end must either be entirely trustworthy, or kept in the dark about his true intentions. What if some of them figure it out and start blackmailing him? What if some elders question him about some peculiar projects of his and he has to defend himself from their inquiries? What if he's actually found out, and has to go into hiding?
This vampire is essentially running a second Masquerade: one that disguises his intentions not from mortals but from other vampires. That's something that could provide plenty of story seeds on its own.
This is likely to have competition
Assamites love to eat whomever they can get their hands on. Various clans hate each other, and would love to destroy the other clans' progenitor. Some clans are afraid of their own founder (like the Nosferatsu), and some might try to destroy them themselves given the chance. And other vampires without a 3rd generation member in their ranks (like the Baali) would jump at the chance to have an Antediluvian's power backing them up. In short, the idea to diablerize (or at least destroy) an Antediluvian is one that several people have come up with: and your character will need to beat them to it.
What if a faction of some clan or another starts working directly counter to this character, trying to steal the information they've gathered? What if they get to information he needs first, and he has to steal it from them? What if he starts getting to close, and they send assassins to try and kill him to stop him from reaching the Antediluvian first? What if they frame him for a breach of the Masquerade, and he has to clear his name while hiding his true intentions from the Camarilla authorities? All of these things could generate stories and be the source of interesting conflict.
Antediluvians are protected
In the dark ages, two Antediluvians were diablerized by younger vampires. Since then, the Antediluvians may have taken measures to ensure they are difficult to reach again.
Perhaps they have used powers of domination to enthrall entire famliy bloodlines, creating societies of mortals which will defend them. Perhaps they used ancient magics to make their resting places inaccessible except to those who possess secret keys or artefacts. Or perhaps they simply slumber in incredibly inhospitable locations, burred deep in the ocean floor or in unstable precarious caverns.
Gathering resources to overcome these obstacles could generate stories. And even if they are all prepared for, the Antediluvians themselves could present a challenge. Will this character be prepared if the ancient one was suddenly to awaken? Will they have the means and might to overcome them? This could be a final battle of an epic campaign, or even an end to an act but not the entire story if the Antediluvian proves too powerful and escapes.
Still, let them try
This vampire has a goal which is sure to alter the entire world if they succeed, and likely will alter the world even through an attempt. But that doesn't mean that you need to have this world altering event any time soon! All of these obstacles could take years or even centuries to overcome. After all, several other vampires have been trying to do exactly this for thousands of years, and it usually doesn't work.
But that being said, let him try! The game of vampire allows us to set lofty ambitions, and it could be very fun for them to make incremental progress, feeling that they are closer and closer to their goal. If they are clever and ruthless, careful and creative, they may actually one day succeed! But, like the goals of other ambitious vampires (like "I want conquer all mortal nations" or "I want to control all religions" or "I want to become the last vampire on earth"), these goals are not going to be accomplished quickly or easily. Doing so in a vacuum would be hard enough, but in the World of Darkness they'll also have to contend with the various forces attempting the exact same thing.
Someone once said that the biggest problem with conspiracy theories is that they posit some particular group "controls everything": that's not to say that there aren't powerful forces, or sinister schemers, or shadowy figures out there in the world. The problem is there are lots of them, and they are all fighting each other for control. This character is now one of them. Welcome to the Jyhad, young one. Many have walked the path you now seek, and stumbled.
Will you be the first of this age to complete it?
Only time will tell.