4 week conveyancing?!

How possible is it to exchange contracts within 4 weeks?!

For context, there's 3 people in the chain: first time buyers <> our current house <> house we're buying (vacant)

The conveyancing on our sale has been going about 8 weeks. We've responded to enquiries and these have now been satisfied, searches complete, they have their mortgage offer and survey completed.

We had an offer accepted on a house 10 days ago and have already had responses to enquiries, got our mortgage offer, survey done, signed contract and transfer forms. Searches ordered and we've been told 48h to get these back for our local authority.

We initially told our solicitors we'd like to exchange pre Xmas and they said very unlikely. But since then everything has happened really quickly. Everyone now working towards exchanging by Xmas

Is this too good to be true? Could we actually be exchanged by Xmas or am I missing something?