Disclaimer: This method uses commands, so create a copy of your world and use it there, or else you will no longer receive achievements in your world.
time query command can be used to check the in-game days that have passed since you created your world. You can also check the number of ticks that have passed since you created your world.
/time query day
Shows the number of in-game days since you created your world. (Each day lasts 20 minutes, 10 minutes of day, 10 of night.)
/time query gametime
Shows the number of ticks since you created your world. (One tick is 1/20 of a second.)
How to create a copy of a world:
1. Open the setting for your world by pressing the "pencil" button. (You need to leave first)
2. Click on the Game settings tab.
3. Scroll down to the bottom, and click on the Copy World option.
4. You should now see the copy of your world in the worlds menu, named: "Copy of
Name of your world"