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2019 F250, Gas 6.2, 15k miles. Put key in and roll over to start. Nothing. No clicks, just nothing. Take key out and try again, nothing. Take key out and try again and strong roll over and starts. It don’t happen every time but at least once a week. Installed a new battery, same problem. All the normal bells go off when I install the key. Does it have a starter relay somewhere other than the starter solenoid? I hate intermittent problems.
In the meantime until it does it again, id start with checking the starter connections. Back them off and then reseat and snug them up. Next time this actually happens turn the key over and no crank, see if with the key still turned over and your foot on the brake you can shift to neutral and start the truck. There are other things to check with a voltmeter when its actively happening, but until then I wont send you on a wild goose chase to most likely find nothing because its starting up normal.
Sounds like a ignition switch or starter going bad or a bad electrical connection in the starting circuit. First thing to do is get a comprehensive scanner hooked up to it and see if it's throwing any fault codes. If that doesn't show anything, I'd start at the battery and pull all the cables on both ends, clean and coat them in dielectric grease and do the same thing to any wires and plugs in the starting circuit. You could pull the starter and get it tested, but where it's intermittent it might test OK. This sounds like one of those issues you either throw parts at, or wait for a total part failure to single it out.
When you turn the key to the start position you are not directly engaging the starting circuit. You are sending a signal to one of many control modules telling it that you want to start the engine. The control module engages the starting circuit. But first!, the control module checks several things including communication with other modules. If it doesn't get the right responses is does not engage the starter circuit. An important diagnostic step is to check for any error codes that may indicate a bad control module and/or communication path.