what does it mean when a time series cannot be converted to a stationary process? Disclaimer: I am a new learner when it comes to time series.
Typically, before obtaining summary statistics like the mean, or applying models like ARMA, you would want to transform your time series to a stationary process using differencing or log transforms.
But consider that your time series follows a sigmoid shape. In this case, no amount of differencing will convert the time series to a stationary process. I assume this is because the time series is not resultant of a (potentially latent) continuous random variable with a fixed mean and variance. But rather a variable that is a function of time.
Because of this, you are not able to do any kind of ARMA modeling, or determine summary statistics like the mean.
What happens then? Can you just not do any analysis on it?

It depends on the length of the time series. For instance, if I have only six months of temperature data, then I cannot use an ARIMA model to forecast the other six months, as the data I have so far does not fully pick up the seasonal pattern.
On the other hand, if I have three or four years worth of data, then the seasonal pattern can be more easily detected.
In this regard, I would try expanding the length of your time series to determine the best model. If you are working with only a few minutes of data (as seems to be the case in your comment) then the data simply is not exhaustive enough to infer characteristics of the time series over a longer period.
