Cross-section experiment with Differences-in-Diffrences estimation I am trying to answer the following question related to econometrics:
We have a sample consisting of a cross-section of individuals in 2016 plus another cross-section of different individuals in 2018. We believe that, in 2017, a natural experiment took place affecting individuals of a particular type (the ‘treatment group’) and not affecting individuals of other types (the ‘control group’). Both types were present in our two samples. We are thinking of running a differences-in-differences estimation.
I would like to know whether:

With the sample that we have, is this estimation feasible?
If the estimation is indeed feasible, then why so?

If possible, please provide a detailed answer, for me to go over.
Dif-in-dif (DiD) strategy relies on the identifying assumption of parallel trend. This essentially means that in the absence of the treatment, the control group and the supposedly treatment group would have evolved similarly (ideally both in the pre-treatment and post-treatment period). The information you provided did not mention anything specific to this underlying assumption. If the systemic difference you mentioned introduces some differences in levels between the control and treatment group but nothing else, i.e. they evolve similarly notwithstanding the difference in levels, then you can use the dif-in-dif. More generally, the dif-in-dif strategy assumes there is no other time-varying factor affecting the groups other than the introduction of the treatment.
There are other things that should also be taken into account when doing a dif-in-dif study. Is the assignment of the treatment affect the control group? Does the composition of the treatment and control groups change as a result of the treatment?
For a more comprehensive yet approachable analysis of the DiD strategy, you can have a look at chapter 5 of Mastering Metrics: The path from cause to effect by Angrist and Pischke (2014).