As a fellow sniper, I'm trying to max out McCready. I have not got his quest yet, not sure when or how to get it.
Just continue to adventure and quest with him. Depending on what and how you play, getting companions to like you can be quick or slow. Companions will like or dislike you doing certain actions of traits, e.g. taking chems, picking locks, hacking terming, indiscriminate killing, being charitable, using persuasion, showing loyalty, stealing etc. The game will tell you if you've done one of those things, e.g.
Codsworth liked that. Surprisingly for a post apocalyptic dog-eat-dog world most of the companions are fairly moral by the benchmark set by modern civilisation so if you're playing a complete dick it's going to be a slog. Maccready is a bit of a rogue and likes you
picking locks,
using charm in conversations and
stealing but he dislikes
indiscriminate killing.
Most characters have two of three 'friendship stages' and you know when you've crossed into a new stage because the character will generally try to initiate a lengthy dialogue (by the game's standards) about how things are going. At this point some companions, including Maccready, will also have a quest which you can pursue to move things on further like romance. Romancing pixels isn't my thing so I've not pursued that side of companions.
I've been taking each companion with me until I max their friendship/loyalty (which generally gives a perk) then moving to a new companion. The perks remain even when you've not with that companion.
edit: as a sniper myself, Maccready is not a great combat companion because he also likes to hang back which involves many enemies rushing both of you.