Early Train from Bruge to Amsterdam

Google maps gives just under 3 hours drive from Brugge to Anne Frank House, but with no concern for traffic issues, parking issues, or any other problems you might run into. Since you first have to exit Brugge, and won't be able to park anywhere near Anne Frank House, assume significantly longer.
It claims your walk from Amsterdam Centraal to Anne Frank House is 18 minutes, but again there is no accounting for the physical abilities of you and your group.
DB Bahn shows the earliest train as you described, actually arriving 10:04 (leaving either 5:08 or 5:57 AM, I do not recall from being in Brugge recently if you will be able to get transit to the train station that early). You can get there earlier by taking a late night train (between 10:30 and 11:30 PM) from Brugge, but this does not arrive until 8 AM.
The same Google maps suggests that you can get from Centraal Station to the Anne Frank House by car in 5 or 6 minutes, but I have no idea how long it will take to de-train and get a taxi.
I doubt that the Anne Frank tickets can be exchanged. I think you need to reconsider your lodging logistics, or else accept an all-nighter that includes a several hour layover in Antwerp, among other transfers.

Thank you. It's helpful to know you couldn't find another easier route. I think we may need to spend the night in Amsterdam if we want to use our Anne Frank tickets...

Another option would be to drive to Antwerp and take the 6:45 IC train that gets to Amsterdam Centraal at 9:04.

Enjoy your time in Amsterdam. The Anne Frank House is a must see and it is good you have a reservation and get to bypass the massive line. It is not that long of a self-guided tour so you will have time to possibly go to another museum or attraction.

I have to be honest that I actually found the Dutch Resistance Museum to be more moving and very emotional at times. It takes about an hour and a half to really read through and take in every exhibit, but it is well worth it. I learned a lot as it was very thought provoking. There was no line to get in, at least when I went in late May. I think this would be a good complement to a visit to the Anne Frank House if it fits your schedule.

I think the best and more relaxing option is to go to Amsterdam the day before the visit. You can drive to Antwerp the same day, but doubt if you can drop off the car there so early. A taxi from Bruges to Antwerp for catching an early highspeed train is possible, but is it worth the costs and hassle?

The stress and hassle of getting from Bruges to the Anne Frank House in time isn't worth it. You are on vacation and you should relax. As other posters have suggested, stay in Amsterdam overnight and enjoy the city.

Thank you all for your suggestions! I will look into hotels in Amsterdam.

I'm going to swim against the current here.

With arrival at the Anne Frank Huis around 10 am, I think that a car trip with three people is probably easier and less stressful than a tight train connection in Amsterdam.

Because it would be important to me and because if the traffic gods smile on you it can be done in less than 3 hours, I would count on 4 hours. Leave Bruges at 6am, everybody use the toilet before you go.

Getting out of Bruges is easy, even with the Sint Michaels road works. Straight on for Gent, turn left for Antwerpen. You will be through Antwerpen before traffic gets heavy.

Route via Utrecht, not Rotterdam unless you want traffic. Into central Amsterdam and park at P1 opposite Centraal Station then you can take tram 13 or 17, or bus 170, 171 or 172 to the Anne Frank House. Get off at the 'Westermarkt' stop, and walk to your right to the Prinsengracht canal.

I think you can do it if everybody is disciplined and only make one rest stop, and make it a quick one.

Remember the speed cameras, even if you have Belgians examining the inside of your tailpipe, and that variable speeds in the Netherlands need to be observed to avoid a ticket.

My friends from Montana think nothing of driving 90 minutes to go out for Chinese food! But it makes no sense to drive or train 4 hours each way for a day trip to a city in another country.

A crucial omission is whether you have ever been to Amsterdam before? Because I think Bruges is over-rated (that's a bias) I think you should change your Vacation plans to spend more time in Amsterdam, if you haven't been there before. I suppose you have your plane tickets, so you can't fly out of Amsterdam anymore.

As I see it, the penalty of being too late arriving is severe. You have to spend the night. BTW, we were unwise enough to drive to our well-located B&B before returning the car in Amsterdam. It was a nightmare of one-lane, one-way streets, with trucks unloading and blocking the street, not to mention narrow passages and mysterious instructions from our own Garmin GPS. The last four miles will be the worst part of a car journey. Research parking garages and tram lines now.

I'd go along with Amsterdam really being too far for a reasonable day trip, and that it makes sense to stay overnight.

I'll disagree over with Tim about Bruges being overrated, though. Granted, it's personal preference but we preferred it to Amsterdam, and think it's well worth spending some time in.

Regarding the costs it’s understandable to do this daytrip by car. You will visit Amsterdam on a Saturday (18/7), so there will be less trafic so I don’t expect serious congestions. If I am informed well prebooking P1 near Amsterdam-Centraal railwaystation will costs €20/24h and fuel will be about roughly €50, so in total some €70. Preparing well and facing no setback it must be doable, but question remains I think if it is not too much of a hassle just before a such an intense experience as the visit to the Anne Frank House is, so hard to say if it will be reasonable this way.