Based on the docs the getComponent method should be called during initialize. Becase it's a Promise the method initialize should be async.

When the component loads very quickly, this.component will be undefined in connect:

import { Controller } from '@hotwired/stimulus';
import { getComponent } from '@symfony/ux-live-component';

export default class extends Controller {
  async initialize() {
    this.component = await getComponent(this.element);
  }

  connect() {
    console.log(this.component); // undefined
  }
}

Adding async connect won't solve the problem. Adding a small delay will solve the problem. Another way is to call getComponent inside async connect. Either way, the documentation is a bit "obscure" about this and devs without a good JavaScript understanding will have the same issue.

I don't know if this is a bug or the way Stimulus work, but I was expecting that connect will be called after initialize resolve.