How can I lookup and modify a Cloudfront distribution using the CDK?

How do I lookup a cloudfront distribution using the CDK? The only option I see is

    const distribution = cf.CloudFrontWebDistribution.fromDistributionAttributes(stack, "DataApiDistribution", {
      domainName: "...",
      distributionId: "...",
    });

Neither domainName and distributionId is known by me in this context, so how can I solve this? Things I do know about my distribution:

• What tags it has,
• what domain it is exposed as in route53

When I have the distribution, Id like to add more origins to it

import * as cf from "aws-cdk-lib/aws-cloudfront";
import * as route53 from "aws-cdk-lib/aws-route53";
import * as route53Targets from "aws-cdk-lib/aws-route53-targets";


export default function DataAPI({ stack, app }: StackContext) {
  const host =
  stack.stage === "prod"
    ? "data.mydomain"
    : stack.stage === "dev"
      ? "data.dev.mydomain"
      : "data." + stack.stage + ".dev.mydomain";

  if (app.region === "eu-north-1") {
    // Create CloudFront distribution
    const distribution = new cf.CloudFrontWebDistribution(stack, "DataApiDistribution", {
      originConfigs: [
        {
          s3OriginSource: {
            s3BucketSource: myBucketInEUNorth1,
          },
          behaviors: [{ isDefaultBehavior: true, viewerProtocolPolicy: cf.ViewerProtocolPolicy.REDIRECT_TO_HTTPS }],
        },
      ],
    });
    const hostedZone = route53.HostedZone.fromLookup(stack, "domain", {
      domainName: app.stage === "prod" ? "mydomain" : "dev.mydomain",
    });

    const endpoint = new route53.ARecord(stack, "DataApiAliasRecord", {
      zone: hostedZone,
      target: route53.RecordTarget.fromAlias(new route53Targets.CloudFrontTarget(distribution)),
      recordName: host,
    });
    // Output CloudFront distribution URL
    stack.addOutputs({
      CloudFrontURL: endpoint.domainName,
    });

    return {
      URL: endpoint.domainName,
    };
  } else {
    // Here I need to lookup the CloudFront distribution created in eu-north-1 and add origins to it

    return null
  }
}