Out of curiosity did you order the black or blue color? Regardless I congratulate you on an excellent choice of phone! The Pixel 4A and the prior 3A series has further convinced me I no longer need a flagship device. I absolutely love the 4A and have no regrets.
For two weeks I was rocking the phone naked and while I could have kept going like this I chose to get a case primarily because I want a higher value for my phone if I can keep it in mint condition and choose to sell it later. The black version (which I have) does develop smudges from the oil in your hands and I also have a feeling the coating on the plastic would begin to get a shiny look after a long time if rocked naked. The 4A does have some grip but again the oils in your hand can make it slip after a while. It all comes down to your preference and how comfortable you feel needing to replace a device if it got serious damage from a fall or general scratches that are bound to happen. Even if it is made of plastic you might end up dropping the phone on its face or corner of the phone and a case would definitely minimize that damage.
You can always use a dbrand skin if you don't even want a case at all.
If you do opt for using a case I can recommend the below minimal cases.
Very thin case that feels similar to the back of the 4A without smudging. This was the first case I bought:
https://www.amazon.com/X-level-Goog...ag=hawk-future-20&ascsubtag=UUacUvbUpU6930734
This is the second case I just bought and have been using for a week just because I wanted to try something different. It's just slightly thicker than my first case but is both aesthetically and physically nicer:
https://www.amazon.com/Caseology-Va...ag=hawk-future-20&ascsubtag=UUacUvbUpU6930734
As for tempered glass protectors this is the one I use because I wanted a protector with a cut out for the front facing camera:
https://www.amazon.com/Screen-Prote...ag=hawk-future-20&ascsubtag=UUacUvbUpU6930734
Hope this helps!