What time does the tube begin in the AM?

The first service leaves Notting Hill Gate at 05:08. You would need to change at Edgware Road and would arrive around 05:30.

later if it's a Sunday

https://tfl.gov.uk/modes/tube/first-and-last-tube

A black cab or mini cab door to door wouldn't cost very much for that short distance.

"We will need to take the tube to St. Pancreas Station"

BTW, it's St Pancras, nothing to do with body parts:-)

On our departure day a couple years ago, we headed for the tube early in Muswell Hill, North London, and soon realized that the first train did not go all the way to LHR-we were right away losing twenty or thirty minutes. It worked out but the lesson was to make sure, especially, as someone mentioned, if it's a Sunday (or very early), that the route you want is served when you need it.

The 7:01 to Paris only runs weekdays.

Anyone going for the first train weekdays at 05:40 will find their public transport options a bit limited though.

Thank you so much everyone! We are going on Tuesday, September 8. I am thinking it might be a better idea to use a black cab. Silly me, naming a tube stop after body parts☺️ My bad!

You could also consider a private car service. You would be given the cost before you book the reservation. We have used Blacklane.com. It includes the tip also. They are based in Berlin, but offer private transportation all over the world.

Note that Blacklane doesn't run any transport itself, it sub-contracts behind the scenes via a reverse Dutch auction to local companies. I can't see in London where the advantage would be over booking with the well-known minicab companies.

Well, I had heard that London was going to catch up with NYC and have 24 hour tube service, but I see that it is only for Friday and Saturday nights on certain lines....Nice for those who are partying, but I guess shift workers in London are still outta luck. Interesting.