Google has been restoring a smart speaker giveaway since last year (via Android Police). However, at this time, the company offer is available to a larger number of people, with a simpler sign-up process in place as well. To find out if you are eligible for a free Nest Mini, all you have to do is visit this webpage.
The giveaway is open to active individuals and students of YouTube Premium, YouTube Music Premium and Google Play Music subscribers. If you are the primary account holder of a family plan, you can also get a free Mini Mini. The promotion is open until June 30th, though Google warns that it may end earlier if supplies run out. So far, it appears that only people in the US can take part in the giveaway. It said the terms and conditions did not cite any restrictions in the region, so Google could use the offer in additional countries.