Transportation Liverpool to Manchester Airport

I would not spend the last night in Liverpool with a 10 AM departure in the offing the next day . Go the night before and take a room in Manchester , preferably at the airport

There isn't a train early enough- the first one at 6am arrives at MAN at 0725.
It's 50 miles, I would ideally not even want to go that distance by cab in case there was a motorway problem.
If you can change your Liverpool hotel to a Manchester one that would be preferable.

I don;'t think it's necessary to have an airport hotel overnight, although you could if you leave it until a late train the night before. mA hotel near Piccadilly station would leave you with a simple train ride the morning after for your flight. Or come earlier as there is plenty to see and do in Manchester as well.

Thank you all so much for the responses.

Perhaps I was looking at the wrong train schedule, the earliest I had seen was 8 am which struck me as unusual. I will check again. Thank you.

We will be at the Open the entire day before we leave. Given the event, taking a train back into Liverpool for luggage, and then catching another train to Manchester, I was unsure of changing hotels that night as well as it would likely be quite late. The distance between the cities looks approximately the same as the drive to our local airport here in the US hence I thought driving that morning would be workable. I will take a look at the airport accommodations recommendations I saw posted on another thread.

On another note, you will not be checking your bags through to the U.S.

In Dublin, you will go through U.S. immigration and customs. You will also go through TSA type security. When you arrive in the U.S., you walk off the plane as if it was a domestic flight.

https://www.dublinairport.com/flight-information/travelling-to-usa

What you could do is to leave your luggage at Liverpool Lime Street left luggage office that morning, before you go off to Hoylake for the Open, then collect it that evening on the way to Manchester.
If you are flying home on Sunday 23 July then the first train from Liverpool would indeed be the 0815.
But if you are staying for the last day and flying home on Monday 24 July, then there is the earlier train.
If you are flying on the Sunday then the first train from Manchester Pic to the airport is at 0735.
If you'd stayed in Central Manchester on the Saturday night you would have to catch the bus #103 from Piccadilly Gardens at 0550, which arrives at the airport at 0638.
On a weekday there are far earlier trains MAN to the Airport.
On a Saturday the last train from Liverpool to Manchester or Manchester Airport is at 2319 (or 2300 airport direct).

By the way, even on a Sunday National Express run a direct Coach from Liverpool One Bus Station (opposite Albert Dock) to Manchester Airport #170 at 0530, arriving at the Airport at 0630- for the princely sum of £3.50.
The previous coach is at 0245.

Thank you so much for the recommendations! I will look into them.

I was aware that we would do our US immigration in Dublin. I had been told that we would not pick up our luggage, but images would be shown to us for confirmation of checked bags. I had not heard of anything like that before, but I also have not checked a bag in 20 years. Thank you for the link.