I’d be happy too (although it’s not Thomistic - it is a different Scholastic, Scotus)
Firstly - an infinity of things that are essentially ordered is not possible.
This is so because of what is called an infinite regress
Secondly - and as the totality of caused things that are essentially predicated by causation is itself caused;
All caused things belong to a Finite group or “totality” of things which can be said to be caused. All “red” things belong to the totality of “red” things, like this all “caused” things belong to the totality of “caused” things.
Thirdly - it must so be caused by some cause which is exempt and distinct from this totality; for else then the former would be the cause of itself; for the totality of dependant things is cause; and distinctly not on anything belonging to that totality - for that would entail a contradiction;
This “totality” cannot have caused itself, so it must be caused by something that is outside this totality. If something is outside the totality of caused things it must not be a caused thing; in the same way that something outside the totality of red things must not be red
Fourthly - Thus, the extra-total cause itself must be predicated by a lack of prior causation essentially
An intrinsic part of this external cause is that it is NOT caused (see above)
Fifthly - for else it must be an element of the composite of the totality of caused things etc
If this external thing WAS caused this is a contradition - something cannot both be caused and NOT part of the totality of caused things.
So - An extra-total (totality of contingent essence) cause exists.
Now, I can formulate this in regards to reality - we percieve things that are caused; I plant a seed and a vegetable grows - this vegetable is a caused thing. This vegetable and all other vegetables etc. are caused things, this an every other caused thing belong to a totality of caused things. This totality is finite - because an infinite cannot be created by 1+1+1+1 etc. - it will never be infinite. Now, then this totality must be caused by something UNCaused (see above) - there we have our creator.