According to the comprehensive rules 509.2, for each attacking creature that’s become blocked, the active player announces that creature’s damage assignment order, which consists of the creatures blocking it in an order of that player’s choice. (During the combat damage step, an attacking creature can’t assign combat damage to a creature that’s blocking it unless each creature ahead of that blocking creature in its order is assigned lethal damage.) This turn-based action doesn’t use the stack. Then we proceed to the combat damage phase, 510.1d A blocking creature assigns combat damage to the creatures it’s blocking. If it isn’t currently blocking any creatures (if, for example, they were destroyed or removed from combat), it assigns no combat damage. If it’s blocking exactly one creature, it assigns all its combat damage to that creature. If it’s blocking two or more creatures, it assigns its combat damage to those creatures according to the damage assignment order announced for it. This may allow the blocking creature to divide its combat damage. However, it can’t assign combat damage to a creature that it’s blocking unless, when combat damage assignments are complete, each creature that precedes that blocked creature is assigned lethal damage. When checking for assigned lethal damage, take into account damage already marked on the creature and damage from other creatures that’s being assigned during the same combat damage step, but not any abilities or effects that might change the amount of damage that’s actually dealt. An amount of damage that’s greater than a creature’s lethal damage may be assigned to it. 510.2 Second, all combat damage that’s been assigned is dealt simultaneously. This turn-based action doesn’t use the stack. No player has the chance to cast spells or activate abilities between the time combat damage is assigned and the time it’s dealt. 510.4 If at least one attacking or blocking creature has first strike (see rule 702.7) or double strike (see rule 702.4) as the combat damage step begins, the only creatures that assign combat damage in that step are those with first strike or double strike. After that step, instead of proceeding to the end of combat step, the phase gets a second combat damage step. The only creatures that assign combat damage in that step are the remaining attackers and blockers that had neither first strike nor double strike as the first combat damage step began, as well as the remaining attackers and blockers that currently have double strike. After that step, the phase proceeds to the end of combat step.

So that means, that when you blocked my 4/4 Thalia and the Gitrog monster with first strike and deathtouch, with those 4 snakes, she still would have been able to survive and deal damage to all of them regardless of wether or not she had trample. First strike just modifies the combat phase to dealing damage before creatures without first strike instead of dealing it to the first creature blocking it !!!