I'm making an alien race that's kinda like the Tyranids. My problem right now is that they're starting out on a planet. How would they actually leave this planet using only their biological abilities? Note that I'm designing this race as one that relies on extremely fast evolutionary stages (EX; an adult creature sees a need to survive in a colder climate, so it rapidly evolves itself)
Consume the Dying Planet
Your species might realize that the planet is dying and evolve to consume it while it's still useful. A massive queen-like individual slowly eats the planet, evolving to use its immense energies as propulsion. Housing her children inside herself, she sets out to find other worlds.
A rockoon is a rocket lifted by a balloon. This allows the space vehicle to traverse the thickest part of the atmosphere before launch, reducing the energy required to escape.
You could have huge floating balloon beasts. Which every alien world should have anyway. Their metabolism generates hydrogen internally which is where they get the lift.
A team of balloon beasts would float the spacecraft as high as they could go. These balloon beasts would of course grow in size as they ascend and the pressure decreases. They could have the capacity to generate internal heat, adding some hot air balloon aspect to their lift.
I am not aware of any animal that produces fire. But: neither are there hydrogen balloon animals. Moving along: once at maximum altitude the balloon animals contract, pressurizing their hydrogen stores. They and the ship begin to fall. The balloon animals now vent their hydrogen in a controlled way, igniting it as it passes through a shell-like siliceous burn chamber. This rockets the creatures through escape velocity.
Now they are out in space. How to move along? Yes: balloon animals once more. The inhabitants of the ship include several and as they generate hydrogen and oxygen they vent it, propelling the ship along with small bursts.
This would be slow. Also your ship should be comprised almost entirely of balloon animals and their food and drink. These things would not be super scary when they arrived on your world. Unless you are my old dog Toby who was terrified of hot air balloons.
- But: these are your Tyranid equivalents and they are mutable and versatile. The balloon creatures could simply be one morph they are capable of. It would make a lot of sense, once in space, for the balloon beast spaceship never to re-enter an atmosphere but instead shoot re-entry capable seeds or spores at any likely world they perceive. These seeds would land and begin to accumulate biomass in the most efficient way which could be done via evolution: each seed could randomly develop into some morph which would do its thing and produce more of its kind. If you had a sunny world then a photosynthetic morph would do well., A world with lots of tiny prey would support a giant filter feeder. A world with larger prey could support a predator. A world with only inorganic minerals would support a chemoautotrophic slime.
The evolutionary barriers to such a creature evolving by chance seem immense. But something like this could be designed by intelligent agents.
The main challenge is that on a planet they can breathe but in space they will have to develop a way to transport their gas required for breathing with them. A possibility would be that the species starts out with small air packs like some Water breathing spiders do gradually develops ways of either transporting more air in large hollows of their exosceleton or to reduce their whole metabolic activity while in space thus requiring less air. Alongside they would have to adapt to the low temperatures. How much depends on the planet of origin's temperature.
A subset of the species could develop flight and then eventually orbit. Similar to the beetle that can shoot hot acid at its enemies by mixing two inert compounds just before attacking, this would just be on a much bigger scale.
In order to survive space travel it would help if they can hibernate for millennia. Staying active during space travel usually is wasteful and the energy requirements for space travel is much lower if such extreme slower transfer is ok.
In addition to the other answers they could also utilise natural phenomena for transport. e.g. ride on rocks that get ejected from volcanos to get into space (only a very small fraction will - but biologicals have time), and ride solar wind into interstellar space.
If you want to stick with the Tyranid concept - consider the method they function in the game's lore (taken from Lexicanum website):
Capillary Towers are Tyranid plants that reach the upper atmosphere (and beyond). Where they grow, Reclamation Pools then start to appear. The towers are linked to them via underground roots. Later, the towers link up with the sucking proboscis feeding tubes of hive ships in low orbit, which then pump the biomass upwards and distribute it to the waiting biovessels.
The capillary towers are capable of growing in the deepest of seas, able to sustain the pressure of the depths and the coldest of waters. As they grow the planet's tidal flow is altered by their powerful metabolic filtration systems, used to draw all biomass.
So, if your species will be using capillary towers after becoming space-faring, maybe that's how they've got to space in the first place - their home planet became a single interconnected network which devoured all organic matter. As there was nothing left to consume, it started reaching upwards - until it was able to form it's first space-faring organisms at the top of some of its towers...