Was it possible for Jack Sparrow to escape from Davy Jones’ Locker if the others had not come for his rescue. This came to my mind as he was able to come to the sea on his own.
It's unclear, really.
Firstly, Jack Sparrow had earned his place in The Locker, after being eaten by the Kraken, and Damned by Davey Jones. He had been placed there specifically, by Davey's/The Kraken's "magics". When the crew came to rescue him, they were mortals coming to rescue a damned soul, and as is the case in most situations with entrance through a back door to the afterlife (or similar places), throwing living people into a place where there should be none, kinda messes things up a bit. The crew (i.e. the living) had the ability to leave of their own accord, through the backdoor they opened to get in, and their arrival could have potentially started the ball rolling for Jack (emphasis mine):
The Locker was used by Davy Jones to relegate souls that either refused to join his crew or Jones himself deemed unfit to serve aboard the Flying Dutchman. The interior of the Locker represented a soul's worst fear, so its appearance was believed to be perceived differently by everyone who entered it.
For Jack Sparrow, the Locker was a vast expanse of hot sand, on which he and his ship, the Black Pearl, were marooned with no hope of reaching the sea. Here, Jack was confronted by several hallucinations, each one presenting various aspects of his persona, created to send him mad over time. This punishment played on Sparrow's love of the sea (in that he equated it with freedom), along with his pride in being "the one and only" Captain Jack Sparrow.
From memory, the crabs appeared only after the crew had managed to make their way towards the entrance into the Locker; perhaps as they entered through the portal. (I personally believe these two events are linked).
However... he was not the only one to escape
There are two other pirates within the PotC universe have also escaped: Black Bart and Jocard, whom both appear to have been freed in some way, due to Jack's intervention with them in one way or another. There is no evidence or understanding as to how either of them escaped, but it was only after they ran into Captain Jack:
Jack Sparrow later encountered Black Bart in Davy Jones' Locker, after the former was taken there by the Kraken. [...] The two subsequently fought, and Roberts was defeated by Sparrow. After being stabbed by Sparrow, Roberts gave a maniacal laugh and then, simply disappeared, leaving only his boots and sword behind.
Jocard lost all hope of being free, until another imprisoned Pirate Lord, Jack Sparrow, tracked Jocard down and dueled Black Bart. Sparrow won the duel, and freed Jocard from his cell. It is unknown how Jocard escaped the Locker, as he was not onboard the Black Pearl when it escaped, and neither did he have the mysterious navigational charts of Sao Feng.
The problem here is that there is a lot of magic involved in this whole adventure. Mythical monsters and gods and parallel dimensions, as well as many hints that Captain Jack Sparrow may certainly be more attuned to all of it than most. Most are in it for their own glory, whereas Jack simply wants to enjoy the freedom of sailing the high seas; a master of the ocean, and second only to the power of the sea.
EDIT: MissouriSpartan raised a good point about the crabs being a connection point to Calypso, which actually explains the crabs in the Locker (emphasis mine):
On the quest for freeing Jack Sparrow from the Locker, the crew led by Barbossa captained the Hai Peng into World's End. They landed in the Locker, where Jack Sparrow noticed that the Pearl was being dragged across the sand by crabs. The ship reached the crew with the help of the crabs that were actually under the control of Calypso. After escaping the Locker, the Black Pearl went on its way to meet with the Brethren Court.
This is how Jack arrived at the ocean, with the Black Pearl - it was specifically Calypso (i.e. Tia Dalma) that brought Jack to the ocean, to meet the crew.
 Captain... Captain Jack Sparrow.
 We're still talking about Captain Jack here, not the monkey.
No, he couldn't. Let's take a look at what was needed to actually escape the locker
A Ship (or boat) in the water
Yes Jack had the Black Pearl but he was neither near water, nor had the crew to actually operate it (remember those clones of him weren't real). In order to get out of the Locker he would need to get it in the water and successfully turn it upside down which leads into the next point
In order to turn the ship upside down he would need multiple people, he can't turn the ship upside down with only himself.
The knowledge to get out
The only reason any of them escape The Locker is because Jack successfully figures out the riddle "Up is Down" had he not had the map and had he not looked at it, they'd still be stuck in there
To be in the water
Let's also remember that, again, the only reason any of them get out is because Tia Dalma successfully used her crabs to get the boat from on the sand to in the ocean. Had they all arrived there, with the map, with the ship still miles or km away from the ocean, they'd still be stuck there.
Since Jack had none of that we can conclude that no, it was impossible for him to escape The Locker alone.