As far as I remember the cycle went like this: Leathery egg. Face hugger. Implanted embryo. Gut-wrenching infant. Leathery, egg-laying Queen. We know the humans studied the aliens. Was there an in-universe (movie, comic, novel, video game) explanation of how solitary aliens were able to reproduce?
There have been two alternative reproduction cycles that have appeared in the movies that show how individual xenomorphs can reproduce without the need for a Queen:
The directors cut of Alien: There is a famous scene (deleted from the theatrical release) which shows Ripley discovering a barely-alive Captain Dallas and the body of Brett. They have been cocooned by the xenomorph, and are both mutating into one of the original eggs capable of creating a facehugger. This shows that a single xenomorph can use a victim for food and/or to continue the egg -> facehugger -> chestburster -> xenomorph -> egg life cycle.
Aliens vs Predator: Requiem: The Predalien (a xenomorph born from a Predator) is shown in this movie to have the unique ability to use it's second set of jaws to implant embryos down a victim's throat, thus bypassing the egg and facehugger phases and allowing a Predalien to directly spawn other xenomorphs. It's not specified where this ability comes from (possibly from the DNA coming from the Predator host).
From my understanding xenomorphs are incomplete DNA wise, they evolve and advance by assimilating the DNA of the host. So while individual aliens take on the characteristics of the species they were incubated in, the race as a whole follows the normal life cycle of egg > facehugger > full alien, with "queen eggs" making "queen facehuggers" etc.
This is one of the reasons Predators loved using Aliens as prey. 1) They changed with each new species they are exposed to and 2) they sit dormant in their eggs for as long as necessarily.
In the novel Prey (Alien vs. Predator Book 1) we are occasionally taken into the minds of the predators. The main predator thinks to himself that when a bunch of xenomorph males are in close proximity to each other, one of them will morph into a queen. The first Alien vs. Predator movie is loosely based on this novel. The most notable thing copied is the Predator branding the human with the mark of the clan (for fighting prowess).
This is presumably what also happened in the movie Aliens. The colonists investigated the ship and a number of xenomorphs were spawned. The xenomorphs would take some of the colonists back to the derelect spacecraft and more xenomorphs were spawned. Eventually the all male population produced a female, which took up residence in the warm and humid atmospheric reactor.
My interpretation was that the eggs were largely self-supporting after being laid, so they could just sit there dormant for years or decades - maybe longer - waiting for some nub to wander in. The movies provide no evidence of face-huggers hatching without a potential host nearby, and I don't recall any situation in the comics where that occurs.
It's easy to see the hibernation concept in the first and second movies. It takes decades for Ripley to get home, and for a third of that time there are colonists on the planet - who have no contact with the Aliens, it's not until Ripley gets back and Burk sends the colonials out there that they get infected.
The third movie skips the egg process, as Ripley and Newt are already infected by the time they go into the deep freeze for the journey home. Whether Newt's alien would have evolved into a queen is totally speculation, since it's implied and later confirmed that Ripley is carrying a queen.
It's kind of a 'which came first' problem. There are species in our own world who exhibit similar behaviors, changing sexes as needed, producing queens as needed, etc.
I think they get what they need from the embryos, and if they can't get it they make it...like ants or lizards. So if no queen is available one of them will morph into one.
Quick addition, I was just looking through the Dark Horse AvP comic from 1990. The Predators in that series were flying around the galaxy with an imprisoned alien queen, forcing her to produce eggs, and then using drones to fly down to random worlds seeding them with the eggs...so they'd have more challenging game.
My understanding of it was that a certain percent of the eggs were queens.
The veracity of this is questionable as deleted scenes from the first Alien film depicted the captain of the Nostromo not having been killed\eaten but rather mucused to the wall and apparently implanted with a chestburster. Whether every Alien is able to produce and implant a Queen embryo was implied, it is only conjecture on my part if that was preserved in canon.
The only implicitly stated method to propagate the Xenomorph species was for a Queen egg to be triggered and "impregnate" a host.
A solitary Xenomorph specimen would go through a hormone storm so to speak and mutate in a queen in order to lay the eggs and continue the species. Being as almost all Xenomorphs are female (With some males being noted in the expanded universe), this is easy to see.
Male Xenomorphs are incapable of "switching gender" or becoming a Queen, but they serve as the Praetorian sub-species, which are larger than the standard Drone and Warrior and are noted as the guards of the Queen in a Hive.
I think I recall reading the original novel that references were made to the way wasps stun their prey and then lay eggs in them. This is further evidenced by the deleted scene. I can totally understand the "group of aliens together, with no queen present, one of them becomes a queen" that happens here. I think bees are like that, all female, but sterile unless there is no queen in the hive. However in the first movie, there was only one alien...
The notion of the Aliens genetically morphing biomass into their spores / eggs was the punchline of the original script by Cannon, etc. (The aliens in the screenplay went through even mire lifecycle phases, eventually ending up intelligent enough to build pyramids, etc., after a formative period of voracious feeding. The overwhelming complexity of their reproductive cycle was the Sci fi lynchpin of the original script.) That was changed in the theatrical cut of the 1979 film with the deletion of the famous cocoon scene and other cuts. CAMERON came up with queen idea for the sequel. After that, folks have just to rationalize the two approaches to how the things reproduce.