Is it possible to set the "Start Execution" default JSON input via CDK for AWS Step Functions?

No

Default input parameters are not supported by either Amazon States Language or the Step Functions CreateStateMachine API, though it would be a good feature request.

I'm guessing the default { "Comment": "Insert your JSON here" } is defined by the Step Functions Console, which you will not be able to control.

AWS Step Function exposes an API that lets you programmatically perform operations like invoking a workflow, listing workflows, etc. When you invoke a workflow using the API, you can specify the JSON you want to use. For example, here is the Java API example that invokes an existing workflow.

import org.json.simple.JSONObject;
import org.json.simple.parser.JSONParser;
import software.amazon.awssdk.regions.Region;
import software.amazon.awssdk.services.sfn.SfnClient;
import software.amazon.awssdk.services.sfn.model.*;
import java.io.FileReader;
import java.io.IOException;
import java.util.UUID;
// snippet-end:[stepfunctions.java2.start_execute.import]

public class StartExecution {

       public static void main(String[] args) {
            final String USAGE = "\n" +
                    "Usage:\n" +
                    "    StartExecution <stateMachineArn> <jsonFile>\n\n" +
                    "Where:\n" +
                    "    stateMachineArn - the ARN of the state machine.\n\n" +
                    "    jsonFile - A JSON file that contains the values to pass to the worflow.\n" ;

            if (args.length != 2) {
                System.out.println(USAGE);
                System.exit(1);
            }

            String stateMachineArn = args[0];
            String jsonFile = args[1];
            Region region = Region.US_EAST_1;
            SfnClient sfnClient = SfnClient.builder()
                    .region(region)
                    .build();

           String exeArn = startWorkflow(sfnClient,stateMachineArn, jsonFile);
           System.out.println("The execution ARN is" +exeArn);
           sfnClient.close();
        }

        // snippet-start:[stepfunctions.java2.start_execute.main]
        public static String startWorkflow(SfnClient sfnClient, String stateMachineArn, String jsonFile) {

            String json = getJSONString(jsonFile);

            // Specify the name of the execution by using a GUID value.
            UUID uuid = UUID.randomUUID();
            String uuidValue = uuid.toString();
            try {

                StartExecutionRequest executionRequest = StartExecutionRequest.builder()
                        .input(json)
                        .stateMachineArn(stateMachineArn)
                        .name(uuidValue)
                        .build();

                StartExecutionResponse response = sfnClient.startExecution(executionRequest);
                return response.executionArn();


            } catch (SfnException e) {
                System.err.println(e.awsErrorDetails().errorMessage());
                System.exit(1);
            }
            return "";
        }

    private static String getJSONString(String path) {

        try {
            JSONParser parser = new JSONParser();
            JSONObject data = (JSONObject) parser.parse(new FileReader(path));//path to the JSON file.
            String json = data.toJSONString();
            return json;
        } catch (IOException |  org.json.simple.parser.ParseException e) {
            e.printStackTrace();
        }
        return "";
   }
    // snippet-end:[stepfunctions.java2.start_execute.main]
 }

More examples here:

https://github.com/awsdocs/aws-doc-sdk-examples/tree/master/javav2/example_code/stepfunctions/src/main/java/com/example/stepfunctions