I was able to accomplish initialization by changing searchText type from Subject to BehaviorSubject and initializing value in ngOnInit

import { Component, OnInit } from '@angular/core';
import { Observable, BehaviorSubject } from 'rxjs';
import { HttpClient } from '@angular/common/http';
import { map } from 'rxjs/operators';

@Component({
  selector: 'remote-auto-completer',
  templateUrl: './remote-auto-completer.component.html',
  styleUrls: ['./remote-auto-completer.component.scss'],
})
export class RemoteAutoCompleterComponent {
  searchText = new BehaviorSubject<string>("");
  url = 'https://swapi.co/api/people/?search=';
  results: Observable<any>;
  data: any = [];

  constructor(private httpClient: HttpClient) { }

  ngOnInit() {
    this.searchText.next("John");
    this.httpClient.get(this.url).subscribe((data: any) => {
      console.log(data);
      this.data = data;

      this.results = this.searchText.pipe(
        startWith(''),
        map((value: string) => this.filter(value))
      );
    });
  }

  filter(value: string): string[] | undefined {
    const filterValue = value.toLowerCase();
    if (this.data && this.data['results']) {
      return this.data['results'].filter((item: any) =>
        item.name.toLowerCase().includes(filterValue)
      );
    }
  }
}