¹³ No temptation has overtaken you that is not common to man. God is faithful, and he will not let you be tempted beyond your ability, but with the temptation he will also provide the way of escape, that you may be able to endure it. ~ 1 Cor. 10:13

~ Some Bible versions like the NET Bible use the word trial instead of temptation:

¹³ No trial has overtaken you that is not faced by others. And God is faithful: He will not let you be tried beyond what you are able to bear, but with the trial will also provide a way out so that you may be able to endure it. ~ 1 Cor. 10:13

Question: Will God give you more than you can handle?

There are plenty of passages that indicate that God will give you more than you can handle and the expectation is that you need to depend upon Him.

However what the passages where more than you yourself can handle do not describe the trial of temptation. Temptation seems to be an exception.