Is it possible to get to Diglett's Cave in the sequence suggested by the Pokemon Blue/Red town map?

The sequence of locations in the Pokemon Blue/Red town map (if you just keep pressing the up button) is:

1. Pallet Town

2. Route 1

3. Viridian City

4. Route 2

5. Viridian Forest

6. Diglett's Cave

7. Pewter City

8. Route 3

9. Mt. Moon

...

43. Route 22

44. Route 23

45. Victory Road

46. Indigo Plateau

47. Power Plant

This entire sequence matches the order in which you encounter each of these areas in the normal course of gameplay, with the exception of Diglett's Cave, which you don't normally encounter until later in the game.

Is it possible to access Diglett's cave at an earlier point in the game, as is suggested by its location in the Town Map?

Solution 1:

No, it's not possible to break sequence and visit Diglett's Cave early.

However, the exit to Diglett's Cave (from Vermilion City) is close to the Viridian Forest. You need access to Cut in order to reach it, however, which is not available until after you finish the S.S. Anne in Vermilion City, thus blocking a sequence break there.