In your specific scenario, yes.
As mentioned by John Carroll, you still get the ability to cast Detect Magic without expending a spell slot once per day. That, by itself, is a way to benefit from it.
Generally, rules don't provide any way though.
Usually, if you get the same non-stackable benefit from two different sources, you simply waste the second source. Some exceptions are made in specific texts, e.g. for proficiencies from the background
If a character would gain the same proficiency from two different sources, he or she can choose a different proficiency of the same kind (skill or tool) instead.
With the clarification from Crawford that it's indeed an exception.
The proficiency rule for backgrounds applies when you gain your background at 1st level. It has no relevance outside that context.
Yet, generally, you can benefit from it: How?
Simply: plan ahead. If you are going to take that feat, don't take that cantrip and that spell earlier. You can live until 4th level to learn Detect Magic (usually). If you know you are going to get some kind of feature that provides you a specific, non-changeable benefit, don't get that benefit earlier unless really needed.
Some DMs might give you the easy way as well
It's not uncommon to rule that if you are choosing a feat later in the game and it gives you something that you already had, you can choose something else that still fits the flavor and doesn't break the balance (i.e. same power level). You need to talk to your DM for that, though.
Note about UA
Just a reminder, for this specific case, UA is likely not balanced and not polished in its writing, so you should talk to your DM anyway to check if you're going to be able to use this feat as it is.