Is it possible to construct a USB to UART bridge using MAX232 or TUSB3410 IC?
A MAX232 is a level converter. For your purpose you don't need it.

A TUSB3410 is an USB-to-UART bridge, but a programmable one. You will need to get suitable firmware in the chip. I have no idea how you should do this (an I2C EEPROM seems to be an option), but it is certainly possible. There might even be a ready-made firmware that can be downloaded over USB. On top of that, you will need a suitable USB host driver. Prepare yourself for at least a few weeks of heavy digging. Or a few years of studying programming.

The correct chip for you to use is the FTDI232RL. It is not programmable, it simply works. And host drivers are available from the FTDI website.