Hello cyberirakli!
The FBX plug-in will export the whole time line or a section of it depending on the settings you pick in Maya. In the "Create Geometry Cache Options", you'll see Cache Time Range, if you select a custome Start/End, your cache should not start at zero. You can verify this if you look in the cache folder as long as you set your File Distribution to One file per frame.
Now, as to your problem in Max. Have you tried to manipulate your cash in Max with the Playback Type section of the Pointe Cache Modifier? In my test, I was able to shift the starting of my animation up and down the time line using Custom Range or Custom Start.
Hope this helps,
Regards,
Carlos