diff --git a/lib/internal/http2/core.js b/lib/internal/http2/core.js
index ab961c059187af..a671109b6e7b03 100644
--- a/lib/internal/http2/core.js
+++ b/lib/internal/http2/core.js
@@ -1037,7 +1037,7 @@ function finishSessionClose(session, error) {
   if (socket && !socket.destroyed) {
     // Always wait for writable side to finish.
     socket.end((err) => {
-      debugSessionObj(session, 'finishSessionClose socket end', err);
+      debugSessionObj(session, 'finishSessionClose socket end', err, error);
       // Due to the way the underlying stream is handled in Http2Session we
       // won't get graceful Readable end from the other side even if it was sent
       // as the stream is already considered closed and will neither be read
@@ -1055,7 +1055,7 @@ function finishSessionClose(session, error) {
 }
 
 function closeSession(session, code, error) {
-  debugSessionObj(session, 'start closing/destroying');
+  debugSessionObj(session, 'start closing/destroying', error);
 
   const state = session[kState];
   state.flags |= SESSION_FLAGS_DESTROYED;
@@ -3128,6 +3128,17 @@ 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);
+    }
+  }
   return session;
 }
 
diff --git a/src/node_http2.cc b/src/node_http2.cc
index 5b860a61119d02..9970b1f3d7e341 100644
--- a/src/node_http2.cc
+++ b/src/node_http2.cc
@@ -1829,6 +1829,33 @@ void Http2Session::Consume(Local<Object> stream_obj) {
   Debug(this, "i/o stream consumed");
 }
 
+// Allow injecting of data from JS
+// This is used when the socket has already some data received
+// before our listener was attached
+// https://github.com/nodejs/node/issues/35475
+void Http2Session::Receive(const FunctionCallbackInfo<Value>& args) {
+  Http2Session* session;
+  ASSIGN_OR_RETURN_UNWRAP(&session, args.Holder());
+  CHECK(args[0]->IsObject());
+
+  ArrayBufferViewContents<char> buffer(args[0]);
+  const char* data = buffer.data();
+  size_t len = buffer.length();
+  Debug(session, "Receiving %zu bytes injected from JS", len);
+
+  // Copy given buffer
+  while (len > 0) {
+    uv_buf_t buf = session->OnStreamAlloc(len);
+    size_t copy = buf.len > len ? len : buf.len;
+    memcpy(buf.base, data, copy);
+    buf.len = copy;
+    session->OnStreamRead(copy, buf);
+
+    data += copy;
+    len -= copy;
+  }
+}
+
 Http2Stream* Http2Stream::New(Http2Session* session,
                               int32_t id,
                               nghttp2_headers_category category,
@@ -3054,6 +3081,7 @@ void Initialize(Local<Object> target,
   env->SetProtoMethod(session, "altsvc", Http2Session::AltSvc);
   env->SetProtoMethod(session, "ping", Http2Session::Ping);
   env->SetProtoMethod(session, "consume", Http2Session::Consume);
+  env->SetProtoMethod(session, "receive", Http2Session::Receive);
   env->SetProtoMethod(session, "destroy", Http2Session::Destroy);
   env->SetProtoMethod(session, "goaway", Http2Session::Goaway);
   env->SetProtoMethod(session, "settings", Http2Session::Settings);
diff --git a/src/node_http2.h b/src/node_http2.h
index 79cbe7613b5f6a..306f5460691e06 100644
--- a/src/node_http2.h
+++ b/src/node_http2.h
@@ -694,6 +694,7 @@ class Http2Session : public AsyncWrap,
   // The JavaScript API
   static void New(const v8::FunctionCallbackInfo<v8::Value>& args);
   static void Consume(const v8::FunctionCallbackInfo<v8::Value>& args);
+  static void Receive(const v8::FunctionCallbackInfo<v8::Value>& args);
   static void Destroy(const v8::FunctionCallbackInfo<v8::Value>& args);
   static void Settings(const v8::FunctionCallbackInfo<v8::Value>& args);
   static void Request(const v8::FunctionCallbackInfo<v8::Value>& args);
diff --git a/test/parallel/test-http2-connect-tls-with-delay.js b/test/parallel/test-http2-connect-tls-with-delay.js
new file mode 100644
index 00000000000000..3e2e8a46a3662a
--- /dev/null
+++ b/test/parallel/test-http2-connect-tls-with-delay.js
@@ -0,0 +1,64 @@
+// Flags: --expose-internals
+'use strict';
+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');
+
+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();
+});
+
+server.listen(0, '127.0.0.1', common.mustCall(() => {
+  const options = {
+    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(() => {
+
+      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();
+      }));
+      req.end();
+    }, 1000);
+  });
+}));