How low could kitchen sink sewage inlet go?
No problem and you can go very much lower. It's done everyday for garbage disposals attached to deep sinks and even laundry tubs. I've even seen traps resting on the room's floor with the cabinet bottom greatly notched out for servicing and replacement (plain ugly)...the sink drained exactly like it should and I had no problems washing my tools and buckets.

Additionally, the sink's tailpiece that goes into the trap assembly can be up to a maximum of 24" long. Initially, I couldn't find a public Code Reference, but there is 1 here https://www.law.cornell.edu/cfr/text/24/3280.606 to substantiate this very rarely seen setup.

Your situation seems to be a basement or on-grade slab. Though, if there were a readily accessible crawlspace or garage below the deep sink and its garbage disposal, an up-to 24" tailpiece could place the trap in those areas and not in the sink's cabinet or room at all. In operation and regulation, there's little difference between a sink, shower or laundry standpipe trap.

Side with immediate and easy access in all cases. Not seeing a P-trap in the sink's cabinet will have most Home Inspectors and Newbie Building Code Inspectors hyperventilating and clutching for their red pen. Although, these idiots will still happily approve all illegal horizontal drywall installations, amazingly.