The book intents that the tinkers anvil should only be craftable by the mightiest alloys, yet Creates Zinc-Blocks and XK's Deko Steel block are possible solutions to get an early anvil / good tools.

JEI also claims the tinkers anvil can only be made with slime steel however this is not correct.

I noticed that one too, but if you, i.e. look for recipes using seared stone, you see two recipes for the Anvil.

This was intentional, it encourages playing with Tinkers Construct during the early game.