Это сработало для меня
$ aws2 apigatewayv2 update-api --api-id $API_ID --cors-configuration AllowHeaders="*",AllowMethods=GET,POST,AllowOrigins="*",MaxAge=3600
{
"ApiEndpoint": "https://$API_ID.execute-api.$AWS_REGION.amazonaws.com",
"ApiId": $API_ID,
"ApiKeySelectionExpression": "$request.header.x-api-key",
"CorsConfiguration": {
"AllowHeaders": [
"*"
],
"AllowMethods": [
"GET",
"POST"
],
"AllowOrigins": [
"*"
],
"MaxAge": 3600
},
"CreatedDate": "2020-01-28T17:41:35+00:00",
"Name": "http-api",
"ProtocolType": "HTTP",
"RouteSelectionExpression": "$request.method $request.path",
"Tags": {}
}