Yes, the engine will send the initial game state (player tag, map size and map) to the engine shortly after starting the bot. It does not wait for any input from the bot before doing so. Your 60 seconds timer starts immediately after the engine has sent the data. The 60 second timer is stopped when the bot then sends its name back to the engine.
So do all your initialization after reading the first information from the engine and before sending your name back.
Unfortunately because of the way the starter bots have been structured this was pretty unclear. @Snaar just realized this last night and we began to update the starter bots so the initialization time can be used. So far the C++ and python bots have been updated in github.