You can start it anytime during the one-hour counter begins after the Egg hatches. Best not to start it within the last 5 minutes however in case you run out of time.
You can join in with other people if you start the battle within ~160 seconds or thereabouts of each other (the first person who starts waits that amount of time in a lobby, and then after the time counts down they start regardless of whoever is around). You can also lose a Raid battle and try again as many times as you want for that particular Raid battle without needing another Raid Pass.
Oh, damn, i did not know that you can re-try, i assumed it costs a raid pass each time.
So, assuming that you have enough time and revivers and potions, you can immediately run to a Tyranitar-Raid and just start it and lose if noone else shows up, and then heal up and retry until people show up, in the worst case gaining plenty of practise in how to do most damage with your pokemon.
Raids run for 1 hour and are announced 2 hours earlier by the egg spawn. From what i heared, people generally only go to level 4 raids before the egg is hatched, and once it is hatched, if it is something nice, more people will come a bit later.
The problem with coming late is that people leave after they defeated the raid boss, and everyone tries to be early, most successful raids happen early in that hour.
People are looking mainly for technical machines, so when they go to a level 4 raid egg hatch, they do it even if the pokemon is boring, because a level4 raid gives most stuff and the highest chance for a technical machine.
So i would keep my eyes open for lvl4 raid eggs and try to be there when it pops open and the raid boss appears. Good chances that there will be a group early in the hour after the egg opens.