Mostly up to the GM but...
So there is going to be the standard answer and the extremely situational but possible in game way to accomplish this.
If the DM wills it
Usually, this is the subject a DM would rule on. Ultimately there are DM tools that provide a reasonable path toward celestial status. Now there is almost nothing on becoming a god as of 5e. In lore, Ao has all but banned it inside Abeir-Toril's pantheon. But the DM has tools that can imitate celestial level power or minor deity level power. Boons, Tomes, and Blessings can all improve a character far beyond what a normal character could do. But there is another way.
The Sword of Zariel
In Descent into Avernus you have the opportunity to face Zariel and redeem them or slay them. And how best to do either than with Zariel's Sword. This artifact is picky though and won't just let any ruffian attune to it. You must embody traits desired by the weapon. And if you do, the weapon can be attuned to immediately. Upon that first attunement you basically become a celestial. You gain wings, truesight, resistances, and charisma. In exchange, your personality changes to match and you in a sense become more angelic. Now this doesn't change your type or the plane from which you hail. And it still won't put you on the level of even a minor deity. You will however be a celestial-light character from that moment on. Oh and it can't be dispelled by any means.
So if you're looking for godly power, you gotta go through the nine hells first.