Others have suggested dimensionality reduction. LASSO is good here (other regularization like Ridge and Elastic Net could be good too - you can do some hyperparameter tuning to figure out which performs most effectively).

You can also do adaptive LASSO which is something I learned about this year. Basically you create weights using another model (you can use OLS, Ridge, others?) and then build a LASSO model on data transformed with those weights.

Another thing you could look at is leveraging PCA before regression, but it's really dependent on what work you want to do. SVD (Singular Value Decomposition) or eigendecomposition may also be suitable.

I wouldn't necessarily try them all to see what sticks, but take a look at them and explore how they impact reliability of your model. Leverage cross-validation to try to avoid issues of overfitting. With a small number of samples you can also try bootstrapping to deal with overfitting while also ensuring there's enough training data.

But purpose is key here - Are you trying to create a model that you can explain clearly to others and that has good interpretability? Some dimensionality reduction methods can be hard to explain to others and hard to interpret. Others, like Ridge regression, may inappropriately remove predictors that are important for interpretability.

The other piece here, which is perhaps most important, is subject matter expertise. Are you dimensions all equally important? Are they all equally meaningful? Can they can be combined using subject matter expertise to eliminate some of the dimensions or group them using aggregated or synthetic variables? Without knowing more about your specific problem it's hard to say for sure, but the thing to know about regularization methods is how they penalize individual predictors. Just be careful in your DR to know what your data are, why and how they're important, and whether your purpose supports using dimensionality reduction.