Doing all quest but have a question leading into raids

i have not raided in this game at all but have picked up quests that are going to need a raid to complete. i am assuming lead in quests and quest that move through end game raid will need more than a few people to complete?

since many people in the game are working on current end game, what would be a good way to go about trying to gather people for these quests that have to do with the first round of raids released in ff14?

i am not a leader so gathering people myself wont work, same with the FC im in. is my only choice the duty finder or making a party and hoping someone joins?

Please say which raids do you mean specifically, that'll help with giving advice. :)

Most of the old raids (8 & 24) are still active due to Wondrous Tails, the easiest way would be to joiny any you see in Party Finder for WT or for 24 mans just Que up. (can take 30mins)
Same with the old Alexander tiers, just que up, they are still somewhat active. Or make a PF and note NEW PLAYER BONUS!! people still farming tombstones.

Coil no longer needs progression iirc? so you can do that in any order.

For crystal tower series (labyrinth of the ancients/syrcus tower/world of darkness) and mhach series (void ark/weeping city/dun scaith) you can just queue via DF (you may want to look at videos on youtube if you're not confident) like any normal dungeon. For bahamut and alexander series just make a PF saying first timer, usually some people will help you for the first time bonuses.

If you do decide to form your own raid group in Party Finder, you should understand that the folks helping you are going to assume that you will run the raid with the level sync removed. You can do this by clicking the gear icon in your Duty Finder list, and checking the box marked "Undersized Party". This will both allow you to attempt the content with fewer than eight players if you choose, and also prevents the game from capping your party members' levels to 50. Be aware that running content in this way will make the raid super easy; if you prefer a challenge, and would like to run the content with the level sync in place, it will be much harder to form a party.

As others have said, finding groups to run the Crystal Tower 24-man raids can take a very long time. Possibly even hours, depending on what time of day and what day of the week you are trying for. Unfortunately, there's not really any way to speed this up. Queue up sometime when you have several hours to spare, and while you wait for the party to fill do other content in the game, like Beast Tribe quests, FATEs, crafting, or gathering. Or do content OUT of the game, like reading a book. Just be sure to keep an eye on the game - you don't want to miss your duty commencement once the party actually does fill!

There are various raids, you can either select them from Duty finder once they are unlocked. Some can be 8 man others are 24 man. You need to be more specific. Coil ones are ARR content so you may have a very long wait on those and recommend having your FC help you clear them.