You can use the direct Sofia - Istanbul sleeper, which stops at Plovdiv in the evening and arrives in Istanbul the next morning. There a good guide to the route here

https://www.seat61.com/trains-and-routes/bucharest-and-sofia-to-istanbul-by-train.htm

You can then reach Izmir the same day by ferry + train, or by sleeper train from Istanbul.

https://www.seat61.com/train-travel-in-turkey.htm#Istanbul_to_Izmir

You have to use that train even as there’s no other train into Turkey. There are passport controls in the middle of the night. Buy tickets for it at your local station.

Then I’d recommend reading https://www.seat61.com/train-travel-in-turkey.htm#Istanbul_to_Izmir → by using a ferry and a train you should arrive in the evening in Izmir. (ralderton was quicker than me)