Is it true that Henry Ford forgot to put reverse gear in the first car he made?

This site doesn't precisely explain the reasons for your question, but it does seem to imply that reverse gears simply weren't thought of, or perhaps thought to be of any importance. There were, by the way, several manufacturers and inventors who came out with cars well before Mr. Ford, and Ransom Olds is known to have experimented with the assembly line process before Ford made it successful.

innerauto.com/Automotive_Articles/Automotive_Developments_1895_1907 no longer exists

Apart from the motor, wheels, axles and steering tiller, the vehicle was constructed of wood, and weighed only 500 pounds, without fuel. It had a buggy-like seat and ran on bicycle-size wheels with pneumatic tires. Ford's "horseless carriage" had two speeds - 10 and 20 miles per hour selected by twin drive belts. It had a neutral gear but no reverse. Gear changes were made by a clutch lever mounted on the floor to the right of the driver. Final drive was by a single chain. There were no brakes, but Ford included a doorbell as a horn.

https://corporate.ford.com/articles/history/henry-fords-greatest-innovation-the-quadricycle.html