Articles (an / the / both (an or the) ideal time to do it)

hace 6 años

Hello, everyone!

In the sentence, 

"On the 1st of January 2000, I opened my dream shop. I’d taken (1) - retirement from my job at an insurance company, and (2) the turn of the millennium seemed (3) an / the / both  ideal time to do it."

I need to choose the correct article for the third question. I can choose an, the or even both. I am in two minds which one to choose. 

Could you tell me which answer is correct and why?

Thank you! 

 P.S.: The instruction says that in this exercise it is possible to choose both meaning that both articles are fine. If this is the case could you please explain why?