You just have a class/classes that construct/wire all of your singleton objects and passes the required dependencies into their respective constructors as necessary.
Here is a contrived example of what the wiring code might look like for a web app that uses a database.
public static void main(String[] args) {
MyConfig config = readConfigFile();
DatabaseConnection dbConn = new DatabaseConnection(config.dbHost(), config.dbPort());
UserDao userDao = new UserDao(dbConn);
UserController userController = new UserController(userDao);
List<Controller> controllers = List.of(userController);
WebServer webServer = new WebServer(config.listenPort(), controllers);
webServer.runAndBlock();
}