if a tournament has 10 rounds, and I can only play the first 3 (and in
this example let’s say I win 1.5 points), will my initial rating
become the average of these 3 opponents or will this not count as a
part of my full initial rating?
No and no.
The FIDE rating regulations say
7.14 A rating for a player new to the list shall be published only if it meets ...