Magic Farm (or, more specifically, the MineFantasy mod included with Magic Farm) significantly changes early-game progression. Some crafting recipes are disabled, and early-game vanilla tools are weakened. The normal progression of Wood > Stone > Iron no longer works without a few intermediate steps.
However, if you build a TiCo pickaxe with a stone, flint, or cactus head (all of which can be made in the part builder rather than requiring the smeltery), I think you can mine iron. You can also do this with a blue or green slime pickaxe head, but those are much harder to get in the early game.
The problem with using Tinkers' Construct in the Magic Farm pack is that it completely breaks the pack's intended tool progression.
EDIT:
Hence why the Magic Farm pack is so heavily based on the MineFantasy mod, and doesn't use any mods that MineFantasy's modified crafting and mining progression would break.