Where does “ingress” come from?

Ingress comes from Latin ingressus, formed from the prefix in- and Latin in, tracing back through Proto-Indo-European ne and ultimately h₁én.

ingress (English): The act of entering; Permission to enter; A door...

Definitions

Step	Language	Word	Meaning
1	Latin	ingressus	entered; engaged in; begun, commenced
2	Latin	ingredior	I go into or onto, enter; I enter upon, engage...
3	Latin	īn-	un-, non-, not
4	Latin	în	in, at, on, upon, from (space)
5	Latin	en	lookǃ beholdǃ; reallyǃ?; come onǃ
6	Proto-Italic	en	in
7	Proto-Indo-European	h₁én	in