Travel via train for US citizens from Amsterdam to London

There are as yet no through trains from Amsterdam to London (though there are in the opposite direction), so you always have to change trains in Brussels.
The current timetable is here (see page 3): https://content-static.eurostar.com/documents/446099_Timetables%20Core%20destination_Issue%2082_UK%20EN.pdf

The British government insists that immigration checks happen before you get on the train (that is passport control, not customs, there is no customs as long as the UK remains in the EU). This happens at Brussels Midi station, and the timetables allow time for this.

Your citizenship makes no difference here.

Yes, thank you, I realize we have to change trains in Brussels, however, I wondered if we had to leave extra time for any type of passport control or customs between trains or can we connect as soon as the next segment train is available? I believe the answer is, we only need to hop on the Brussels to London portion and no waiting for any type of governmental checks. Correct? I am inquiring because I would like to purchase the tickets before we leave the US and wondered what time constraints we would be under. Is there a need to purchase before we get there or should we just wait until we are in Amsterdam? I did not want the trains to be sold out.
Thank you so much for helping with this matter.

You can not get to the Eurostar platforms without going through emigration, and you need to do that at least 30 minutes before the train departs.

So when we change trains in Brussels, do we exit and then get back on and need time between trains? I see a train leaving at 8:15 and then it has a connection to London at 11:56, can we take this train? Or will we need to get off and go through passport control and then wait for next train at 14:52 to continue to London? Also the schedule seems to end on May 25 but we will be traveling on 26 May? How can we obtain a schedule for that time?

I wondered if we had to leave extra time for any type of passport control or customs between trains or can we connect as soon as the next segment train is available?

I thought I answered that in my first post. It is two different trains. You will have to get off, and the only way to get to the train from Brussels to London is to go via passport control.
The times I posted above allow time to go through passport control. If you buy a ticket from Amsterdam to London, it will be for both trains, and allow enough time at Brussels for passport checks.

Train No. 9322, depart Amsterdam 08:15, arrive Brussels Midi 10:08
Train No. 9121, depart Brussels Midi 10:56, arrive London 11:57

Is there a need to purchase before we get there or should we just wait until we are in Amsterdam?

It is a lot cheaper if you buy earlier. Prices only ever go up.

we will be traveling on 26 May? How can we obtain a schedule for that time?

If you go to Eurostar's main page ( https://www.eurostar.com ), you can do a query for any date.

I just checked 26th May, and it says "Sorry, there are no seats left on trains going out that day. Can you travel on another date?"

Thank you. Not my plan with hotels already booked but I will have to make changes. Thank you I will go to website and see what I can do.

I’m confused. It seems so simple.

As I look, there are trains on the 26th May from Amsterdam to London that leave at 07.40; 10.40; 13.40; 14.40; 15.40; 16.40.

Choose one.

You change at Brussels. The timetables account for the immigration checks. Just follow the signs and make your way to the connecting train.

Job done.

Fly? I've just checked Google flights, two one way tickets with Easyjet Amsterdam to London Luton (urgh) are £64 for the 26th May (luggage, seating etc would need to be established with Easyjet direct). The price to the more amenable Gatwick is £76 for two or £82 for a more attractive afternoon flight (the previous one lands at 21:45).

I don't know what the prices for the train were but if it was me I'd take the afternoon flight to Gatwick, £41 per person is a reasonable price to me.

Yes, I tried it and all is well, trains are available and I am booking now. Thanks for letting me know that times are built in. Thats what I needed to know. Thanks all for helping here. Happy Travels.

By the way, we are not flying as we have luggage for two weeks and do not meet baggage limits without many extra dollars.
Plus we are interested in seeing the land. Thanks for the thought.

And, by taking the train, you can buy a box of excellent chocolate pralines at Brussels Zuid/Midi to enjoy on the trip.

By the way, we are not flying as we have luggage for two weeks and do not meet baggage limits without many extra dollars.
Plus we are interested in seeing the land. Thanks for the thought.

Ah ok, he baggage issue I can understand however don't get your hopes up too high about seeing the land. Expect miles upon miles of flat farmland and little else and nothing at all when you're in the tunnel. Even the approach to St. Pancras can be quite industrial. Here's an amateur film on Youtube showing the journey from St. Pancras to Paris just to give you an idea of the scenery you'll experience. https://www.youtube.com/watch?v=qlLlw987g9g.

Generally I would prefer to travel by train if journey times are not too dissimilar. London to Amsterdam by train at around 3.5 hours is not too different to an hour flight but including pre-arrival time and transportation from the airport. I merely suggested flying due to the previous post about no availability on the train on the day required. If there are seats or you can alter your arrangements then I agree, travel by Eurostar, zero chance of turbulence which is my absolute fear when flying.

zero chance of turbulence which is my absolute fear when flying.

Turbulence. I don't fear it anymore as I look to the flight attendants for their reaction. When they are calm and either keep working or are told to be seated, I am calm as they have seen it all.