Okay understood, start button label will confuse them if ticket icon gets grayed out, since purchase dialog logic is used in start button too.
But UI design is very easy to do with what. It's very simple. Believe Me. Since you mentioned, currently players gets the feel of starting the game, but buying ticket window gets opened.
How about this,
View attachment 9157
View attachment 9158
it solved the confusion rite, based on ticket availability button label and icon gets adjusted.
Just a thought, if it is not implemented also fine for me. But avoids the confusion for someone.