To the best of my knowledge, no contracts have been let to build the actual railway (track, OHLE, signalling etc), not least because of cost inflation.
So it's not clear when that part of the project will start.
Tunnelling (excluding Old Oak-Euston) is 69.4% complete (50.6km out of 73km).
The most laggardly TBM is Elizabeth, boring the north bore of Bromford tunnel, which has 5.3km more to do - this might take 18 months or so at present rates.
The three stations (again excluding Euston) are not really started yet, although huge preparations are under way.
HS2 Ltd are keeping very quiet at the moment - no PR and no contract news (possibly waiting for ministerial approval).
The first progress report to the new parliament, due in September, will make fascinating reading.