There is no official (or unofficial) indication, and the company has no interest to let us know.
As a TP, you can probably count the rounds in your score history. You, for instance, have two TP rounds, and you had about 35 Pro rounds (estimating).
Later (from Tour Master up) you may want to save the scores (works fine in Excel), because the history holds only 200 scores, including CTTH and Blitz.
You can also write down the RR (ranked rounds) number of the tier upgrade and make an educated guess later.
Last but not least, it's possible to calculate the number from a sequence of score and average data, as long as you aren't "saturated".
But, in the end, this number has no great importance.
- you will plainly see when you are saturated,
- and it doesn't matter unless you match the average threshold.
Most important: Have fun!