Is it ok to use observations from different wave in panel study to do cross-section analysis? Right now I am using data in a panel study to investigate couples' dyadic pattern. I am not interested in longitudinal pattern so I want to do cross-section analysis.
However, this panel study contains many missing values in my interested variables, especially in the initial year, sometimes a row is missing husband data and sometimes it is missing wife's data.
So can I use the observations complete cases (both husband and wife data available) from different years for the analysis？
Or should I use the whole data with multiple imputation and do mixed effect analysis? (I am not very familiar with the mixed effect model, if you could kindly provide the model for me it will be really grateful.)

If you are not interested in within-person factors, it does not make much sense to use the repeated measures of individuals. Your coefficients in a mixed model would be a mixture of within- and between-individual effects for the variables that change within individuals during the panel. If you are purely interested in between-individual attributes and are essentially assuming that observations are static, you might consider taking the average or median values per person of non-missing observations over the period (na.rm = TRUE). This would solve your missing data problem, as well. You would have the option to include each person's lowest, highest, and mean value if that is something of interest for your research question.
