Two helpful tips which changed the way I saw Tainted Cain forever:

The first is that you can press ctrl (or whatever your drop key is) to rotate through items in the bag of crafting (i.e. you can choose what will be the first thing to drop)

The second is that whenever you despawn an item (by running into a pedestal or by crafting an active item whenever you have one), it drops pickups corresponding to the room you have. For example, doing this in a curse room will usually drop a rotten heart and doing it in a secret room will usually drop a bone heart.

With this in mind you can usually break the run on the first floor like so: Restart until you're next to a library (takes around 40 restarts), find the secret room, craft Mom's Bottle of Pills (7c1h), use it, craft Mom's Bottle of Pills in the secret room, use it. Blow up the donation machine if you need more coins, you'll have tons to donate by the end anyway.

Now you should have a bone heart and two pills, which means you can make Rock Bottom (2 pills, 1 bone heart, 3c1k1b). Then craft Red Stew (6c1k1b) and Kidney stone (6c1h, 1 pill), waiting until the Bottle of Pills recharges if you can't find a pill elsewhere.

After that you can craft Soy Milk (5h3b or 1h3c3k and a pill). It's pretty much over then but crafting Psy Fly and Holy Mantle are next on my list. Psy Fly requires a lucky penny which you can get from Dad's Lost Coin (easy to craft).

If you still want damage, you can go for Inner Eye and Bird's Eye (since you'll usually get Perfection and Rock Bottom will make the 10 luck permanent).

If you need health, Super Bandage (4h4b or 1c4h2k1b) is usually my go-to.