Creeper? Aww man

that's why you should always have 2 exits

I do

But I needed to go out that one because my other one is on the opposite side of the base

If you have knockback, you might be able to yeet the creeper far enough to not damage the base.
If you don't, try to equip something that deals a lot of damage, like an axe or sharpness sword to kill it before it detonates

Or use bow and arrow+running for your life

yeah, that's also an option

Well...

My entrance is sorta built into the side of a mountain, and has a fence in around the door, so knockback wouldn't be that effective because I'd still have to open the fence fates.

I can't even get knockback yet because I don't have an enchantment setup

dig downwards, and get far enough for the creeper to despawn, unless it has a name tag.

Average day in terraria