Looking to start running this game. Is Act 1 dependent on at least 1 good card from the first 2 deaths?

The only thing to really be aware of from the first two deaths is that the totem sigils that the woodcarver gives you at the beginning of life 3 is dependent on what sigils you've seen "activated" up to that point ("activated" meaning that Leshy comments on that sigil's ability. So when a flying enemy first attacks, when your cockroach dies, when you sacrifice the blood goat, etc.) She'll almost always offer the Flying and 1-turn buff totems, but the third one you can intentionally choose which you get.

The best ones you can get are Unkillable from killing the Cockroach (the first card choice), the Ant-Spawner from playing the Ant Queen (from the top-right cabinet puzzle), or the 3-blood sacrifice from sacrificing the Goat in a jar (use all your items in the first right, then get lucky getting the goat from the backpack event).

To summarize: die once, then on life 2 decide which totem sigil you want:

• If Unkillable, kill your own cockroach on the 2nd battle (you can play it easily if you get the 4-bones-in-a-jar item).
• If Ant-Spawner, get her from the cabinet and play her in the 2nd battle
• If 3-blood sacrifice, use your 2 items on the first battle before dying, then get goat in a jar in the backpack event. Sacrifice the goat in the 2nd battle.

Then on life 3 you should be offered the sigil as one of the 3 totem options.

You can also get the Many Lives totem by choosing the Cat right after the tutorial and trying to sacrifice it

Has anyone figured out which is fastest? I just got a 32:23 ACT 1 with ant spawner. Having tried most of these it seems the most consistent and least subject to what other cards you get.

People have been having great success with the Unkillable and triple blood sacrifice sigils

by the way I would recommend joining the Discord if you want to further discuss strategy: https://discord.gg/GceyXYCq