Is it possible to contract COVID-19 and heal from it without even noticing it?

Yes, of course. But depending on where you live and when this was, it could also have been an allergic reaction. In the US, Covid really got started in March, which is exactly when things bloom where I am, and pollen allergies set in. I had regular bouts of sneezing, coughing, and sore throat- but I always do in March. Fortunately, this year, I've been vaccinated, so I no longer think it's COVID, but I'm having hay fever symptoms again. 

Yes, it is well known that there are mild and even asymptomatic cases.  But your infection was probably something else.  Probably.  

I doubt you would get over it in one day, unless you had a super healthy immune system. It could have been an allergy or a minor cold. Some people can contract covid and have minor to no symptoms at all. But they usually take more then a day to recover, even if they have minor symptoms. 

I highly doubt that was covid 19, unless you were some how exposed to it. Maybe you should get an antibody test. If you have covid 19 antibodies, then you contracted covid 19. How you got over it in such a short period of time I couldn't know how you did that, without some sort of remedy. 

Yes. That is, in fact, one of the core problems with containing the virus. People might have it and even be contagious without being aware of it.

ONE DAY? No, not possible. You couldn't even have had the flu and recovered in only 24 hours. Those infected with Covid-19 are either totally asymptomatic or have symptoms for several days.

Yes, thousands have.

Far too many "test" positive.

Of the illegal aliens caught at the southern border 1 in 7 test positive, then are released into the USA without further action.

It is possible, but short of an antibody test, it's a safer bet to just go ahead and get the vaccine.  Unless you're allergic, it won't hurt you.

@Anonymous: "Thousands have .." - got any stats to back up your '1 in 7' claim?