With origin edge lambda how to fetch a new configuration without API call

We have a Cloudfront based web application. The application is using Origin Edge Lambda which filters request based on certain SSM parameters. The SSM Parameters need to change often and the lambda fetches it every minute to get the latest value by doing AWS SDK SSM API call. We want to avoid the SSM api call to fetch the value as it adds latency to overall call. What is the best way to store and fetch this frequently changing parameter given the restrictions imposed on edge lambdas ? We do not want to store the value in the lambda itself and go for a redeployment if we have a new parameter value as Cloudfront deployment takes long time.