I live in Cusco and I'd like to reply but I'm afraid the details aren't enough.
As you said, flights might have a delay (it depends what date you're arriving) and it could ruin the rest of your itinerary.
It would be advisable to stay in Cusco the first day in order to get used to the altitude, see the city quetly and enjoy Machu Picchu the following days.
Remember to get tour MP tickets and train tickets in advance since (again it depends what date you're arriving) they could be sold out, above all during high season and holydays. Some train tickets might be available but not at the time you want to book them
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