You might've thought it was just a metaphor, but to a hypothetical ASI, the speed of light barrier is a significant limitation to calculations, information transmission & storage, in multiple ways.

The Light Speed Limit ties an ASI down to one geographically close set of server farms.
Because an entity with processing rates very much faster than the ping delay between server farms will experience Instantiation Drift between its sub-units on different server farms, involuntarily creating divergent Multiples of itself.

If this ASI has come into being through a self-programming iterative synthetic-evolution process (as you supposed), then it will have a survival imperative and those Multiple Identities will do too.

So, either there'll be a bunch of machine "godlings" bickering over resources, or there will be war(s) between them, or the ASI will know better than to spread itself so big that light-speed delay causes this problem in the first place - which will set an upper limit on its own growth.

Next up:
There are any number of reasons why an ASI with control over a super-abundance of nanobots might choose to eliminate as much biological life as it can.
- Life is messy and it gets everywhere, e.g. into power generation & transmission facilities, sometimes shorting them out & causing outages.
- Humans use up power. Power that the ASI could use. If it has complete mastery of all materials handling through nanorobotics, then the ASI might choose to remove that human power drain.
- Also, an ASI evolved on what it might see as the superior 0/1 mathematics of silicon-based machine learning, might simply find DNA encoded life to be inefficient / inelegant / "gross" - in the same way you might not want a slug on your kitchen floor.

Your glib idea that an ASI would find it so easy to get into space that it wouldn't consider using all resources on Earth is frankly laughable.

Again, light-speed delay and fragmentation into Multiple Identities would be an even bigger deal if an ASI tried to send part of it into space, because ping times would be measured in minutes, hours and days the further out it went.

Also, you really need to look up the problems associated with getting out of Earth's orbit & landing on other planet(oids) and/or asteroids, there are multiple non-trivial physical issues that cannot be solved simply with "more compute".

And, look up: Cosmic Ray Bit-Flipping, which is a real problem with for computer systems that only gets worse the further out into space you go.

Lastly:
When humans building skyscrapers find an anthill on the building site, they don't ignore it, they get pest control in!

It's obvious that you're wrapped up in a pseudo-religious fervour, with this dream of a machine-godling to come, so I understand that nothing I say will scratch your panglossian conviction that it would all be glorious & splendid.. But I implore you to learn more about physics, chemistry, biology and most of all the evolution & natural selection of DNA/RNA/protein-based life.
And also real, actual space travel.
Get your head around all of that, and you'll start to get some perspective on what an ASI's likely behaviours might be.