I would ask a question about the sample size to estimate DSGE model
I know that the bigger sample size is, the more informative data is
However, my sample size is quaterly data. In particular, there is a quaterly 13-year data. It implies that I have 52 obs length. So that it is sufficient to estimate DSGE model?

It depends also on the size of your model and on the number of parameters you need to estimate.
For a small model with few parameters to be estimated 52 obs might be enough.
P.

There is no absolute standard. If your are doing Bayesian estimation, your posterior is a weighted average of the sample likelihood and your prior. In this case, you donâ€™t need any observations. The posterior would simply be your prior. Adding observations will help you in updating your prior, i.e. the data becomes more informative, until asymptotically, the prior vanishes and the posterior becomes the likelihood.
The question for you is with which amount of updating the prior you feel comfortable. 52 observations does not sound too bad, but you should expect some parameters to be weakly identified, i.e. the prior you assign will be very important.