Glasgow to Edinburgh late at night

The best option would be to change your booking and spend the first night in Glasgow!

At that time of night, you will have missed the last train, so your options are taxi (expensive) or taking a bus into Glasgow and taking the hourly bus to Edinburgh. It could be 2am before you get to your hotel, assuming your flight arrives on time. It’s not a journey I would want to make at that time of night.

Check travelinescotland.com for your options.

Must you stay in Edinburgh that night? Why not overnight in Glasgow and go to Edinburgh in the morning. If you are staying in a hotel in Edinburgh, will they even let you check in well after midnight?

I did a quick check of train departures Glasgow Queen Street to Edinburgh Waverly (you didn't mention the date you arrive so I checked the schedule for today/tonight) and yes, the last train departs Glasgow at 23:30, so you couldn't get from the airport to the Queen Street Station in time to make the train. The next train departing Glasgow is 5:45 am the next morning (arriving Edinburgh at 6:56 am). You may be young and can do with no (or little) sleep, but if I spent 7 hours and 56 minutes between 11:00 pm and 6:56 am the next morning without sleep , I wouldn't know "which way was up". I didn't look at bus schedules, but the buses between the Glasgow airport and the Queen Street Station may not run at that time, so you might have the cost of a taxi plus a wait in a train station in the middle of the night.