how to expose static directories stored in aws lambda code over API gateway?

I am trying to serve static react app bundle using aws lambda only. I have used a NodejsFunction and applied commandHooks during bundling to bundle a react build along with my code as shown below. I have also attached it to an API gateway as u can see.

  private uiLmbda = new NodejsFunction(this, "renderer", {
    entry: path.join(__dirname, "..", "handlers", "ui-handler.ts"),
    handler: "handler",
    bundling: {
      commandHooks: {
        beforeBundling(inputDir: string, outputDir: string) {
          const staticAssets = path.join(__dirname, "..", "build");
          const relativePath = path.relative(inputDir, staticAssets);
          return [`cp -r ${relativePath} ${outputDir}`];
        },
        afterBundling(inputDir: string, outputDir: string) {
          return [];
        },
        beforeInstall() {
          return [];
        },
      },
    },
  });

  private scanAPI = new RestApi(this, "scan-api");
  private uiGatewayIntegration: LambdaIntegration = new LambdaIntegration(
    this.uiLmbda
  );

And in constructor i am calling this :-

 this.scanAPI.root.addMethod("GET", this.uiGatewayIntegration, {});

Now,i have an index.js as my lambda handler and a build folder with index.html and other refered static files as shown below.

the handler code is as shown :-

import * as fs from "fs";
import * as path from "path";

export const handler = async (event: any) => {
  try {
    console.log(path.resolve("./build/index.html"));
    return {
      statusCode: 200,
      headers: {
        "content-type": "text/html",
      },
      body: fs
        .readFileSync(path.join(__dirname, "build", "index.html"))
        .toString("utf-8"),
      isBase64Encoded: false,
    };
  } catch (error) {
    console.log(error);
  }
};

so i am able to send the html using above handler. but not the relative files as it seems the api gateway is not aware that i wish to render subdirectories from the get method. Any help on how i can do that ? attching screenshots where u can see that main.js ( referenced through html as <script src='/task/var/build/main'><script/> ) gives 403 from api gateway.

Okay, turns out i needed to handle this case in 2 places, one was api gateway and other was lambda handler. I attached the lambda to serve static files using express.static and in api gateway i enabled proxy, and it worked.

Edit: oops! I think i am only returning the index.html from the handler, this way i can only render html, what i needed to do is check the url path from the event itself by reading event.resource key, and send the respective path file from the static folder, would also need to set the content-type header based on file extention