Will not start, when cranking there is white puff of smoke coming from the air intake

Welcome to 2CarPros.

If the timing belt broke when the engine was running, it most likely has internal damage. This is an interference engine. I suspect the white smoke coming from the intake is the result of bent intake valves letting compressed air exit there.

Is it possible for you to upload the audio of it cranking? I can usually tell by sound if there is this type of issue. If not, what I then suggest is to complete a compression test. I suspect you will find cylinders with low or no compression.

Here is a link that shows how to test compression. Do this and let me know what you find. Or, if you can record the engine sound when cranking, that may do the trick for me.

https://www.2carpros.com/articles/how-to-test-engine-compression

Let me know. Also, let me know if you are confident the timing was correct when you installed the timing belt.

Joe