Yes, it is possible. I prefer to set resources, ship construction, and research speed to max. But you didn't specify settings. Assuming everything is set to normal, Here are some tips. Practice until you can get 6-7 planets before the 20 minute mark. The 'impossible' AI players have 3-4 planets at this stage, so you have a chance.
Very first thing, get your free capital ship (I prefer the Sova Carrier, but sometimes I go with the Akkan)
If loyalist, Don't build any frigates until your home garrison has 5 cobalts. Use these and your capital ship to clear nearby planets.
If you went with the carrier, as soon as your garrison has finished producing get a colony ship
Colonize planets as fast as you can devoting resources first to eliminating underdevelopment. Then a research lab for volcanic and/or arctic colonization. Don't bother upgrading the planets beyond the minimum to eliminate underdevelopment at this stage. (About the time I have 5-6 planets I have enough resources to start upgrading more.
Set garrisons to roam (under advanced planet actions)
Target the Javelis LRM Cruisers first then siege frigates. Don't worry about the other ships, just colonize and move on, when you get more resources put up autocannon defense platforms to clear out the others. Don't bother killing or capturing derelict ships at this stage, just avoid their active range and build opposite them.
Grab the planets with the least amount of defenses first
For level 1 research: (not necessarily in this order)
I like modular architecture and asteroid mercantile mandate. I almost never get persuasive offers and think focused exploration is even worse.
I like military grade specs, hull reinforcements, basic provisioning, advanced metallurgy, and shrikens. I almost never get generators, radiation bomb, or jump computer. Psidar usually comes later when I have abundant resources.
After you get garrisons, put up multiple light factories at strategic planets (the more you have the faster they produce)
Don't underestimate Autocannon Defense Platforms. They are cheap, pack a punch and have decent HP. They can also be spammed to create a distraction and keep a fleet from advancing.
If you are fortunate enough to be near a NPC, get broadcast centers early to get tons of free resources.
With the current version, the Carriers are way overpowering, and on tier II to research. Take advantage of this.
If the AI players cooperate, attack in the direction of your orbit.
The toughest game I ever played, my home planet was one asteroid away from an "impossible" AI's home planet. The AI gets very territorial at close range. But so do I. I was lucky I had home planet victory on. I got the planet between us first. The garrison and defense platforms were enough to keep him at bay while I fast tracked a fleet of siege frigates and I quickly killed him. Unfortunately, this distraction kept me from spreading out as much as I usually do, and the other AI captured much of the map.
Keep in mind, it all boils down to resources. The more you get the better. The more efficiently you use them, the better. The more you kill without costing you anything, the better.