diff --git a/lib/internal/http2/core.js b/lib/internal/http2/core.js
index 7260f59868e63a..afd7cd28aafec2 100644
--- a/lib/internal/http2/core.js
+++ b/lib/internal/http2/core.js
@@ -3105,16 +3105,21 @@ function connect(authority, options, listener) {
   if (typeof listener === 'function')
     session.once('connect', listener);
 
-  debug('Http2Session connect', options.createConnection);
-  // Socket already has some buffered data - emulate receiving it
-  // https://github.com/nodejs/node/issues/35475
-  if (socket && socket.readableLength) {
-    let buf;
-    while ((buf = socket.read()) !== null) {
-      debug(`Http2Session connect: injecting ${buf.length} already in buffer`);
-      session[kHandle].receive(buf);
+  // Process data on the next tick - a remoteSettings handler may be attached.
+  // https://github.com/nodejs/node/issues/35981
+  process.nextTick(() => {
+    debug('Http2Session connect', options.createConnection);
+    // Socket already has some buffered data - emulate receiving it
+    // https://github.com/nodejs/node/issues/35475
+    if (socket && socket.readableLength) {
+      let buf;
+      while ((buf = socket.read()) !== null) {
+        debug(`Http2Session connect: ${buf.length} bytes already in buffer`);
+        session[kHandle].receive(buf);
+      }
     }
-  }
+  });
+
   return session;
 }
 
diff --git a/test/parallel/test-http2-connect-tls-with-delay.js b/test/parallel/test-http2-connect-tls-with-delay.js
index 3e2e8a46a3662a..0b3753ae383642 100644
--- a/test/parallel/test-http2-connect-tls-with-delay.js
+++ b/test/parallel/test-http2-connect-tls-with-delay.js
@@ -4,11 +4,7 @@ const common = require('../common');
 if (!common.hasCrypto)
   common.skip('missing crypto');
 
-if (!common.hasMultiLocalhost())
-  common.skip('platform-specific test.');
-
 const http2 = require('http2');
-const assert = require('assert');
 const tls = require('tls');
 const fixtures = require('../common/fixtures');
 
@@ -16,15 +12,9 @@ const serverOptions = {
   key: fixtures.readKey('agent1-key.pem'),
   cert: fixtures.readKey('agent1-cert.pem')
 };
-const server = http2.createSecureServer(serverOptions, (req, res) => {
-  console.log(`Connect from: ${req.connection.remoteAddress}`);
-  assert.strictEqual(req.connection.remoteAddress, '127.0.0.2');
 
-  req.on('end', common.mustCall(() => {
-    res.writeHead(200, { 'Content-Type': 'text/plain' });
-    res.end(`You are from: ${req.connection.remoteAddress}`);
-  }));
-  req.resume();
+const server = http2.createSecureServer(serverOptions, (req, res) => {
+  res.end();
 });
 
 server.listen(0, '127.0.0.1', common.mustCall(() => {
@@ -32,33 +22,29 @@ server.listen(0, '127.0.0.1', common.mustCall(() => {
     ALPNProtocols: ['h2'],
     host: '127.0.0.1',
     servername: 'localhost',
-    localAddress: '127.0.0.2',
     port: server.address().port,
     rejectUnauthorized: false
   };
 
-  console.log('Server ready', server.address().port);
-
   const socket = tls.connect(options, async () => {
-
-    console.log('TLS Connected!');
-
-    setTimeout(() => {
-
+    socket.once('readable', () => {
       const client = http2.connect(
         'https://localhost:' + server.address().port,
         { ...options, createConnection: () => socket }
       );
-      const req = client.request({
-        ':path': '/'
-      });
-      req.on('data', () => req.resume());
-      req.on('end', common.mustCall(function() {
-        client.close();
-        req.close();
-        server.close();
+
+      client.once('remoteSettings', common.mustCall(() => {
+        const req = client.request({
+          ':path': '/'
+        });
+        req.on('data', () => req.resume());
+        req.on('end', common.mustCall(() => {
+          client.close();
+          req.close();
+          server.close();
+        }));
+        req.end();
       }));
-      req.end();
-    }, 1000);
+    });
   });
 }));