Is there a way to reclass after choosing a class for the first time?

While there are no "Second Seal"-type items in Echoes, there are two ways to effectively reclass your units.

The first is the most straightforward-- there is a free DLC pack available that allows you to receive two Villager's Forks, which, when used on a character, will reclass them into the Villager class, which allows you to pick what class path that character will be set on. You could force a character you get later in the game with a set class path into the Villager class and turn them into something completely different.

The second is a little strange, but can effectively give your male units infinite levels. Unlike all other class paths in the game, the Mercenary class path will be able to eventually promote into a Villager class unit. The full tree is

Villager -> Mercenary -> Myrmidon -> Dread Fighter -> Villager

As a result of this, you can class your male units (only male units have access to this class path) into Mercenaries in the beginning, eventually promote them to Dread Fighters, and then back into Villagers, which would allow you to reclass them into what you really want them to be, but with incredibly high stats.