Ground-level electrical wiring to shed outdoors possible?
With rigid or intermediate metal conduit ($$) you can follow code without going very deep - 6" under dirt, 4" under a concrete cover of at least 4" thickness extending at least 6" to either side. Unless you want a concrete path through your garden along the route of the conduit, that's not likely what you want.

Rigid and intermediate metal are tough enough that you won't likely damage them while digging with hand tools.

PVC needs to be 18" under unless concrete protected.

Table 300.5 of the NEC should clarify all that for you.