Yes, you can definitely do that. Just make sure you have clear definitions for your literature search and systematic review. The evidence synthesis in a systematic review can take many forms and if no RCT studies are available, what you are proposing may be of interest. It still does not tell you about causation as you can not overcome the limits of the individual studies by doing meta-analysis.

I highly recommend reading the Cochrane Handbook for Systematic Reviews of Interventions if you plan on doing a systematic review (and meta-analysis).

Yes, you can calculate effect sizes from repeated measures designs, but there are two schools of thought on it. One camp argues that the auto-correlation of repeated measures makes the effect size inaccurate, while the other camp argues that you simply calculate cohen's d using the average of the standard deviations from the paired measures (Time 1, Time 2). This second approach is endorsed by Dan Lakens, in his article "Calculating and reporting effect sizes to facilitate cumulative science: a practical primer for t-tests and ANOVAs" (see formula 10). This approach is also supported by Geoff Cumming. The effect size is easy to calculate, and one can do the Hedge's g adjustment on it. Lakens provides clear commentary on the issues surrounding repeated measures design effect size transformations.

Zhuoxiu Jin It is possible to perform a meta-analysis within only one single group, as long as you have multiple studies that examine the same intervention on the same outcome measure. In your case, you have multiple studies that measure the effect of one intervention on the same outcome measure A. However, it is important to note that the studies being included in the meta-analysis should be sufficiently similar in terms of their design, methodology, and population. It is also important to consider the quality of the studies and potential sources of bias that may affect the results.

In terms of calculating the effect size, using the standardized mean difference (SMD) between pre- and post-intervention scores is a common approach for analyzing pre-post intervention studies. The SMD allows for the comparison of effect sizes across studies that may use different outcome measures or scales.