hunt around, take your time and you’ll spot some good deals. back in January I built up a p-x nanolight with full 105 except for ultegra cranks, p-x model b wheels, vitorria rubino tyres, fsa anatomic wing bars, ritchey stem, p-x twelfty post. Wheighed at the lbs at 18.09lbs with pedals (540s) and 2 bottle cages.
cost was £1050. everything was new, except for seat clamp (new but from my spares bin) saddle (old from spares bin) and pedals (new but from spares bin)
I did get an outstanding deal on the frameset, as the last ones were being sold off, and picked it up for £450. Simiarly the model b wheels don’t exist anymore I think, but there are good deals around (merlin had pairs of ultegra wheels for £209 recently).
check out planet-x, especially good for cheap and okay finishing kit I reckon and often for wheels,
check merlin and rose bikes for groupsets and components, and merlin for wheels.
So yes it is possible, but you have to get really good deals….i was REALLY lucky with the framset!