L.A. Gear, circa 1850.
These Avengers-themed TOMS are unfortunately not real, just a product of the imagination (and Photoshop skills) of awesomely-named Tumblrer Tom Hiddlestunned.
Check out shoes for all six main Avengers team members and Loki -- what, no Nick Fury? -- on Tumblr.
NB: These designs are based on existing TOMS styles, so you could always make your own with a few clever modifications.