From what I've read, if the data is time-homogeneous then I could take the Maximum Likelihood Estimate which is to count, for each row, how many transitions from state i to state j occur in the dataset, and then normalise the rows so they sum to 1.

But not having a mathematical background hinders my ability to do this on my own.

What is time-homogeneous data? and could someone explain what the Maximum Likelihood Estimate is?