@George ******
You are confusing the „visa validity“with the period of stay permit you get stamped into your passport when you ENTER Thailand using the visa.
*** the DTV has a visa validity of 5 year, starting from the day it gets issued
*** on EACH ENTRY within the visa validity, you will get stamped in for 180 days.
The OP didn’t have a DTV when he entered Thailand, so according to his passport country, he entered visa-exempt and got stamped in for a 60 days stay permit.
*** He can ACTIVATE the DTV only by exiting Thailand and re-entering, showing the DTV printout to the Immigration officer at the border.
Then, and only then, he will get stamped in for a 180 days stay permit
He CANNOT activate the first 180 days stay permit out of a DTV while he is inside Thailand.
I have added a picture of a DTV entry stamp.
The OP can wait until the last day of his current stay permit (which is 60 days) before he exits Thailand. He also is free to exit any day before his 60-days stay permit expires, and activate the DTV on his return.