It should tell you on the base of the speaker, somewhere near to the serial number/MAC address.
Alternatively, post setup of the device, in the Sonos App ‘about box’ look for these versions by the device in the list of devices… 

• Play:1 : 1.8 or 1.20
• Sonos One (gen1) : 1.21
• Sonos One (gen2): 1.26

Just out of curiosity, how does it make a difference for you?

I will just add that the Sonos One (gen1) start date is shown online as October 24, 2017 - so if you’re sure the date of the speaker is 2016, then it’s an older Play:1

I wasn’t aware there were multiple generations of the PLAY:1. I thought all PLAY:1s were the same. 

I think there was an increase in memory, at some point, although I don't think they have been labeled gen 1 and gen 2. 

Not totally sure about that though 

Yes same here, originally  I only ever thought there was one main hardware version of Play: 1 (hardware version v1.8) until someone on the forum here showed a photo of a Play:1 with hw 1.20 - so it seems something must have changed. I’m also not sure what altered either, but additional memory seems to be the most likely. I did (once upon a time) have a number of those (excellent) speakers and all were hw version 1.8.x.x