I regret declining a really good PhD offer. Can I ask if I can accept the offer after all?
Dude I am an old guy and here is my advice:


Never be shy to ask for things you don't know.
Accept the fact that you are an imperfect being. You made mistakes, and will make mistakes.
Be open to hear others views, and take moment to digest their words to fully understand their perspective.


Therefore it is totally normal to email the university back with full honesty and tell them that you changed your mind.

BUT before you do that, think twice, thrice or even more. You have already done a mistake for being too quick. Don't be too quick again. At least learn.

To me it seems that maybe you are unstable and change your mind too quickly. Let me blame you a bit: before deciding too quickly, why didn't you just email them back and simply ask "I would appreciate some time to think. Could you please let me know the deadline for my response? Thanks."?

Lesson #1 when you are at a point in time where you need to make a choice, usually the best decision to evaluate and perform is the following:


Evaluate if it's possible to postpone the decision (you might need to ask questions to ensure whether it's possible to postpone the decision).
If it's possible to postpone, then postpone it so that you have more time to think and make a better decision.


Of course, some times it is not possible to postpone a decision because time matters. That's why you need to first evaluate the possibility (or even more accurately: the cost associated with postponing it; if the cost is low, and the value from a more reliable decision is high, then dude postpone it!).