SKILLS at Zero?

Goodman Kettlebriar, be strong!
As I understand the situation, everyone has a 0 Skill points in everything.
If you find a tutor, book, academic institute, special training, etc, and put in the time, then you can apply skill points from Rank gain progressing from 0 to 1 skill point or more.

Our last game system was entirely skill based. You would have next to no chance to perform an action if you didn't have the specific skill. It was frustrating for the players and me as GM. In that very detailed system, I felt we were appeasing the rules to try and play.
TME system is a breath of fresh air in comparison. Why there's even an Accuracy Trait! The rules kind of step aside so that we can just play.

As I understand it, even untrained (or 0 skill points), everyone has a chance to Lie, Grapple, Negotiate, Brawl, Climb, Knife Fight/Throw, use Google, make playdough..

In all honesty, I don't know if I'm handling skill advancement correctly. Once they have achieved the coveted 1 (first) skill point, I let them advance as fast as they wish. It might have taken weeks to gain that 1st point (TME pg 35), but then they are free to spend as they please. *

Edit:
*The ability to put all of your Rank gain skill points in one skill or spread them across your existing skills hasn't been a deal breaker. At first, I thought they would advance way too quickly. Characters could go from removing wood ticks to performing open heart surgery in just a few Ranks, if they want. (The closest my guys have come to actual Healing is one point in Erotic Arts.)
The caveat is the limited amount of skill points available per Rank and the fact that it's difficult to learn/come across new skills.
My guys chose to improve Weapon Expert skills at first and now feel the pinch of slower skill advancement (7th to 8th Rank).