Information on 1.4/1.6 fsi engine and gearbox

Hi everyone, I have recently bought a 1.4 fsi golf and unfortunately it seams like the timing chain has slipped somehow and there is now no compression. It is currently in the garage trying to find out exactly what is wrong and I would like to know that if I need a new engine, would it be possible to fit a BLF 1.6 fsi engine in as they are basically the same just different stroke, the addition of an oil cooler and variable valve timing. I would obviously need an ecu and oil cooler fitted. But I don't know what to do about the gearbox as I don't know if the 5 speed would be okay with the 1.6 as I don't have enough money to change all of the drivetrain. Any thoughts, thank you.
Jack.

why not realign the chain and see if it works first ?

Thanks for the reply. That is what we will be doing. Repairing it is the first option but I'm just exploring the other options in case it can't be repaired or too expensive to repair.