It's two different pools.
A normal man: By the time he's reached adulthood, he has 4 general proficiencies. He may also have some from Intelligence. He will then gain additional general proficiencies from aging. (If you are using the rules from Axioms, he can intensively train to acquire these proficiencies sooner.)
An aspiring adventurer: By the time he's reached adulthood, he has 4 general proficiencies. He has squandered the opportunity to learn a useful trade and instead spent all 4 to get Adventuring proficiency, much to the chagrin of his parents and ex-spouse. He may also have some from Intelligence. At 5th level and thereafter, he will gain additional general proficiencies from leveling. He will ALSO gain additional general proficiencies from aging. (If you are using the rules from Axioms, he can intensively train to acquire the proficiencies from aging sooner.)
A normal man who later becomes an adventurer: By the time he's reached adulthood, he has 4 general proficiencies. He may also have some from Intelligence. As he reaches 2nd, 3rd, and 4th level, he will lose one of his general proficiencies. At 4th level, he will gain Adventuring. At 5th level and thereafter, he will gain additional general proficiencies from leveling. He will ALSO gain additional general proficiencies from aging. (If you are using the rules from Axioms, he can intensively train to acquire the proficiencies from aging sooner.)
So let's take hypothetical hero, HEROICUS, with 16 INT.
1. Heroicus is brow-beaten by his mother into staying home and working as a kennel master for the local lord's hounds. He has Animal Training (dogs), Animal Husbandry, Riding, and Tracking. Because he has 16 INT, he has two other proficiencies. Because he hates his life, he is prone to spending lots of time alone in the woods, and takes Naturalism and Survival. After 5 years as a kennel master, he gains another proficiency. He takes Animal Training (dire wolves) and fantasizes about being recruited by an evil dark lord and training a pack of wargs to devour the village bailiff.
2. Heroicus is a rebellious youth and rejects the counsel of his parents to get a day job. Instead he apprentices to Oldmanicus, a retired ranger, and becomes a 1st level explorer. He has Adventuring proficiency instead of 4 general proficiencies. He learns Precise Shooting as his starting class proficiency and Tracking as his starting general proficiency. He has INT 16, so he chooses two more general proficiencies, selecting Riding and Survival. At 3rd level, he gains a class profiency and chooses Combat Reflexes. At 5th level he gains another general proficiency and chooses Endurance.
3. Heroicus is depressed he's become a kennel master. (He hasn't been at it for 5 years yet). One day, Oldmanicus is called out of retirement, and he invites Heroicus to come along as his henchman. Heroicus agrees and soon becomes a 1st level explorer
- At 1st level, he has: Animal Training (dogs), Animal Husbandry, Riding, and Tracking, plus Naturalism and Survival . He gains a starting class proficiency and chooses Precise Shooting. He does NOT gain Adventuring yet, nor another general proficiency.
- At 2nd level, he must give up one general proficiency. He abandons Animal Training (dogs).
- At 3rd level, he must give up one general proficiency. He abandons Animal Husbandry. He also gains a class proficiency at this level. He takes Combat Reflexes.
- At 4th level, he must give up another general proficiency. He abandons Survival. He now gains Adventuring. He now has - Combat Reflexes (class), Precise Shooting (class), Adventuring, Riding, Tracking, and Survival.
- At 5th level, he gains a general proficiency. He chooses Endurance. Note that Heroicus is now finally at the same spot he would be in #2 above at 5th level.