Can I estimate a generator matrix Q of a Continuous Time Markov Chain using discrete time without an absorbing state?

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I have discrete time data with 7 states and none are absorbing. Is it possible to estimate the generator matrix Q of the CTMC using the discrete time data? My concern is that the examples I've seen have a default state but mine doesn't. If so, what is the process and will the constructed CTMC be Markovian?