Your sources of Seals right of the bat are:

- FATES

- Daily Lvling Roulette

- Daily Guildhest

- Grand Company leves

- Grand Company Hunting log.

By far the quickest source will be the Hunting log though you wont be able to get all the entries. I think around 4 of the entries in the first section are in Halatali, a lvl 20 dungeon, so one run of that should net you a good chunk of the Seals you need.

Outside that doing your roulettes and doing the Grand Company Leves are probably your fastest way to get more together.