There's no evidence to show that it wasn't impossible for non-trapped players to gain access into the game. What Kayaba Akihiko did was removing the "Log out" option and altering the game so that the death flag would cause the NerveGear to fry the player's brain.
Of course, whether it was possible or not on the basis of what Kayaba did to the game is one thing, the other factor to consider is the authorities.
When Kirito first entered Sword Art Online, he was on his bed. However, at the end of Aincrad arc, he woke up in hospital as seen where he wakes up and stumbles out to look for Asuna.
It was also mentioned that the NerveGear has it's own internal battery in it which accounts for 30% of it's weight, in the Novels it's revealed this battery has atleast 10 minutes of power in it being one of the conditions set to kill a player.
In the novel, Kayaba announces to the players that if one of the following happened: being disconnected from a source of electricity for 10 minutes, cut from the system for more than 2 hours, or dying in-game, the NerveGear would fry the player's brain, killing them in the real world.
Soruce: Episode 1 - Adaptation Notes (Point 2)
Kayaba also says how people outside the game were told to avoid forceful removal of NerveGears yet some chose to ignore this (though it doesn't imply he cared for their lives).
Having informed the outside world of the situation beforehand, [Kayaba] reported that friends and family members of some of the players had already ignored his warning, causing the death of 213 players, showing images of the SAO incident.
Source: Episode 1 - Plot (7th paragraph)
Also every trapped SAO player was moved to hospitals within the first 2 hours of the game starting as a respone to Kayaba's announcement to monitor their condition, and for those who didn't die in-game, to keep them from becoming under-nourished.
He also told them that his crime was being broadcast all over the world, with the location of each player, thus the authorities would be moving them into hospitals to put them in better care during the 2 hours he had allowed the players to be disconnected from the system.
Soruce: Episode 1 - Adaptation Notes (Point 2)
In the Novels, to which the anime does not mention, SAO was only released in Japan so the only players effected were Japanese. in the Wiki it says that after the SAO incident NerveGear had been seized and disposed as according to Japanese Code of Criminal Procedure, Article 121
all of this indicate that the Japanese Authorities were well aware of what was going on and would be in the public's best interest to prevent any more cases of players being trapped inside. in terms of the game the Authorities didn't need to stop people getting more copies of the game as only 10,000 copies were first produced and 10,000 players were trapped1
Only 10,000 copies were printed in the first batch of the game, and online sales sold out within seconds. Hard-core gamers waited in line for days to purchase the first few hard copies from many stores.
«Sword Art Online» officially started server service at 1 PM of November 6, 2022 and obtained infamy when the creator succeeded in trapping 10,000 people in the game, and making it so that death in-game would mean actual death for the player.
Source: Sword Art Online - Background
however on the NerveGear Wikia page it states there were about 200,000 players in possession of a NerveGear, so i assume that the authorities seized about 193,853 NerveGear during Death Game (3,853 from the player who died)
This next part is mainly speculation. However, Cardinal system, which could possibly corrected new players entering the game, since we didn't see outside authorities trying to help players in-game with clearing all 100 floors. though this could be them being cautious as effectively Kayaba was in control of 10,000 lives
It is also mentioned that Kayaba has a level of honor and fairness so i would assume that as he aided players to reach the 95th floor (where he would reveal himself as the final boss) he would also act on any outside interference against anyone in some way if they came up with hacks designed to help beat the game or attempt to back into the game itself.
Akihiko had a level of honor and fairness. He designed Sword Art Online to be a beatable game by anyone who had the skills. He never interfered with the players' progress to keep them from advancing through the game; in fact, as Heathcliff, he was actually fighting on the players' side, helping them clear floors. The one exception to this is the fact that he made himself invincible until his battle with Kirito, although this was necessary to survive the game until the 95th floor was reached, where Heathcliff planned to reveal his true identity and become the final boss on the 100th floor.
Soruce: Kayaba Akihiko - Personality (4th Paragraph)
1: the web version of the story which included the adult #.5 chapters says there were 50,000 players trapped