Why doesn’t God just prove himself to me if he’s really there?

This question hinges on understanding God’s purposes and considering His perspective rather than a creature perspective.

God’s purpose at this time is not to “prove” Himself.  At the appointed time that will come for all men and be resolved instantly, at death or at His appointed end of the age.

His purpose at this time is to find men & women with a heart suitable for His eternal purposes.

God looked down from heaven upon the children of men, to see if there were any that did understand, that did seek God. Holman Christian Standard Bible  Psalms 53:2

New American Standard Bible
“I, the LORD, search the heart, I test the mind, Even to give to each man according to his ways, According to the results of his deeds.

“I the LORD search the heart and examine the mind, to reward each person according to their conduct, according to what their deeds deserve.”

Jeremiah 17:10

But the hour is coming, and is now here, when the true worshipers will worship the Father in spirit and truth, for the Father is seeking such people to worship him.  John 4:23

And without faith it is impossible to please God, because anyone who comes to him must believe that he exists and that he rewards those who earnestly seek him.  Hebrews 11:6

The fool says in his heart, “There is no God.” They are corrupt, their deeds are vile; there is no one who does good.  Psalms 14:1

For since the creation of the world God’s invisible qualities–his eternal power and divine nature–have been clearly seen, being understood from what has been made, so that people are without excuse.  Romans 1:20