Does casting a Subtle Spell count as surprising a target if target does not know you are caster?

I understand you can’t Sneak Attack with spells, something to do that both abilities scale thus game breaking. So that takes away one aspect of my predicament. However the Assassinate ability still gives Advantage over lower initiative targets, and according to Can an Assassin use Assassinate with ranged spell attacks?, an assassin with surprise will auto-crit with a spell.

If you have the Subtle Spell metamagic, can you still Auto-Crit with a spell attack after the start of the encounter if the target doesn’t know you’re a spellcaster? Does casting a Subtle Spell count as surprising a target if target does not know you are spellcaster?

For example: as an Assassin 3/Sorcerer 3, at start of encounter I shoot a target with a light crossbow and Hex spell, dealing 1d8+2 damage. Target has yet to see if I or any of my allies is caster. Next round I use Chill Touch at same target. Do I auto-crit and roll 2d8 cold damage +2d6?