All's good, just don't forget that you need a link between несмотря and a follow up clause.

Несмотря на то, что...

Несмотря на + noun/pronoun works just fine as is.

Some minor things for the sake of style:

Работа goes better with сделать or закончить

сделать работу (most common for finishing a job) - закончить работу

завершить работу - wouldn't recommend using it without merit, it kind of has a different shade of meaning here, though not tangible enough to describe. Or maybe it's just not something you hear too often, so that's why it rings the bell.

Also дело has a bit of a different vibe there. It's more like a deed or task, than job (in the meaning of something you do as a part of your official employment).

Moreover, поздно начать can mean that it was not a late start but that you started something late as in time of day Context can usually clarify what you mean anyway, it's just a "so you know"

All in all, here's my shot at tranlating this:

Несмотря на то, что мы начали позже, чем нужно, мы сделали работу.