Sadly, you can’t actually have one. No original airworthy examples survive although there are replicas.
One can however experience part of the starting process. Modern jet engines are usually started by an APU, a small gas turbine mounted in the tail and which you’ll hear running as you board a plane. The Me 262 had proto APUs in the form of Riedel two stroke flat twins, one mounted in a nacelle at the front of each engine. You started the Riedel electrically or with a recoil starter if necessary and then used it to spin up the jet engine.
Being rather smaller than a 262 (or any of the other planes equipped with it) quite a number of Riedels have come down to us still operational. Like this one.
Yes, they went on to start it electrically later but they did establish that you could start your 262 just like your lawnmower.