how can I cache ID tokens from cognito for subsequent hits to API gateway? : how to implement this scenario in AWS?

the user hits a API endpoint in API gateway, Cognito is used for verification. the user passes access id (after successful Cognito verification) to API gateway, then once the access token is exchanged with id token, can the id token be cached in API gateway or elastic cache for subsequent API hits to avoid the overhead of token exchange for each call?