Creationism

[GrandizerII]

Does the first cause/mover/pink unicorn "exist", does it have a kind of "existence"?

Overlooking the "pink unicorn" bit and therefore treating this question seriously:

According to Aquinas: my understanding (and it's always open to correction because I'm a dummy when it comes to Aquinas' metaphysics) is the first cause is basically existence that grounds the existence of everything else. So yes, it exists, but in the sense that its existence and essence are one and the same thing (unlike us beings that require the act of existence to be conjoined to our essence by something else). And it has no potential to "not exist".

According to WLC/Plantinga/other theistic personalists: Generally, the first cause exists eternally and necessarily. It is not absolutely simple like the Thomistic version, but it too would be metaphysically impossible to "not exist"

And if you're asking for my view: still thinking about it. The metaphysical position I tentatively hold to atm doesn't "care" whether there's a first cause or not. Perhaps existential inertia is a thing after all, and no first cause is needed to sustain the existence of anything, I don't know.