Role of T-Statistic in a T-Test

I am not sure if my reasoning about T-Statistic is correct. Could please review it?
T Test is defined as a test for checking how unlikely a difference between two groups’ averages is occurred because of random chance in sample selection. The T-Statistics is the number that the T-Test provides, defined as (mean - Null Hypothesis)/Standard_Deviation where Null Hypothesis is 0 because we the null hypothesis is that the group have the same average.
If this number, in absolute value term, is big the T-Test is stating that is highly unlikely that the difference between two groups averages is occurred because of random chance. Therefore we can reject the null hypothesis