Assuming the obvious things have been checked like fuel, spark plug, fuel line obstruction, and air cleaner, the most common reason for small engine starting issues is fuel not being drawn through the carburetor.
If you prime the engine with a small amount of fuel, and it starts right away, you have fuel delivery issues.
These engines rely totally on suction, for fuel flow. If the suction is not sufficient, it will not start.
This problem can be caused by lack of compression, or the choke not closing all the way.
The choke causes all the suction to be used to start the fuel flow. Check to see that it is adjusted to fully close, when the lever is in the choke position.
I Have owned a 1964 Bolens 600, for 30 years. I have modified it in to a 10 hp with hydraulics. It is mostly retired now, but it is a great little tractor. :thumbsup: