That is a very tight, but not impossible schedule if everything goes to plan.

Please keep in mind that this is Latin America, and there are lines everywhere: check in, security, and the world there does not move with the expediency that you get accustomed to in North America, Asia or Europe.

That may sound trivial and condesending, but I wish someone reminded me of it - it is not like UPS - The World on Time.

If you have the ability to buy yourself an extra day to allow as lag, it will make your visit to MP more enjoyable.

Remember - you need to arrive in Cuzco, take a 2 hr train ride to Aqua Calientes, then a 20 minute bus up the slopes to get to MP, then repeat in reverse to get back to Cuzco and the airport back to Lima.

In my opinion, there are many opportunities for delays and missed connections. There was a warning at the Cuzco airport that flights sometimes do not run on time in the PM. I have a photo of it in my Trip report.

The Hiram Bingam train does do day trips, but it is outrageously expensive.

Try Packages from Peru Rail to help with planning.

Good luck