Try the coach (National Express). Easier than the train (best route for the train is Elizabeth line to Farringdon. Thameslink to Gatwick. The Gatwick Express is a waste of money. There is only one escalator to navigate from Elizabeth line to Thameslink. I usually buy separate tickets. Tap in LHR tap out at the top of the escalator from Elizabeth line. You may need to go up to ground floor to descend to a southbound platform. I'm usually northbound.

You can not save any time via the train, it's just more jumping luggage.
Other opinions are available. I took the coach in Jan.