Completely possible.  I consistently top score as an F2P(Kinda lucky with the Mk conversion update though, which changed my m2.10 aka mk6.10 into mk7 instead, allowing me to begin the grind for mk8.)
- Stop playing when done with missions
- Upgrade a single combo.  Potentially 1.5, but not two.  Gameplay will get boring though.  You can explore other combos with an alt account.  
- Don't buy useless things like paints, gifts, etc.
- Don't buy drones, you run out of batteries and it needs to be upgraded.
- Upgrade during and not during sales, and don't buy speed ups.  In general, the middle few upgrades should be on 30% sales, and last few 50% sales.  If you only upgrade during sales, have fun waiting years.  
- The following overrules the above tip.  Exception of not buying a speed up is when, for example, you upgraded something that takes 25 hours at the start of a sale.  Nearing the end of the sale, you can speed up and buy the next upgrade if it is an overall positive trade in the long term.  
- Get good.  Turn your turret, game sense, etc.
- Save your containers and weekly containers.  Save all your containers for when you have a lot of time to play, such as holidays or summer.  If you get premium, you have the time to grind.  The higher the rank of opening weekly containers, the more supplies and crystals you get, even if you got them at a lower rank.  
- Don't bother with stars for the battle pass.  It is nearly impossible with no premium, not worth it without a battle pass, and you will run out of supplies.  
- Restart your account if must.  
 
GLHF.