With Fire Edit alone, no. You have to level your units up from level 9 to level 10 and use a Second Seal while at level 20 to learn the tier 1 class skills. To learn tier 2 class skills, just level up from level 4 to level 5 and from level 14 to level 15. Because of this, you can't permanently...
Is there a way to get a unit to level 0 to permanently learn the tier 1 class skills? Or any other method for that matter?
As far as I can see, Fire Editor can assign a skill to a unit, but it's only "temporary". As in if you were to remove the skill you put in, it'll disappear.