No, but NOT simply because it is an instantaneous spell
It might be argued that because the spell has a duration of instantaneous, you cannot be at the same time both within the line and within ten feet of the line. However, this reasoning fundamentally misunderstands the nature of instantaneous spells.
'Instantaneous' as a spell duration does not mean that the spell itself takes no time. Instead, the definition of 'instantaneous' is:
Many spells are instantaneous. The spell harms, heals, creates, or alters a creature or an object in a way that can't be dispelled, because its magic exists only for an instant.
Features do (only) what they say they do. The only thing a duration of instantaneous means is that the spell is too short to dispel. It does not mean the spell cannot have different but sequential effects within the same, undefined, 'instant'. This may be counterintuitive to a natural sense of the word 'instantaneous', but it is what the word means as a defined game term.
As proof of that, we have other instantaneous spells that call for sequential effects. Consider the Lightning Lure spell, which has a duration of instantaneous (emphases mine):
You create a lash of lightning energy that strikes at one creature of your choice that you can see within 15 feet of you. The target must succeed on a Strength saving throw or be pulled up to 10 feet in a straight line toward you and then take 1d8 lightning damage if it is within 5 feet of you.
In this case there is a far range effect that provokes a save, if that save is failed the target is moved, if the target is moved sufficiently it ends up in the range of a new effect and then it takes damage. The movement and damage take effect at separate, discrete points in time despite the fact that the overall spell is 'instantaneous'; the damage comes after the movement and only if the result of the movement brings the target sufficiently close.
If 'instantaneous' duration meant that no time could pass during the period of a spell's effects, then lightning lure could not both move and then, depending on the results of the move, damage a target. To put it simply, within the duration of the same instantaneous spell, the target is both more than five feet from the caster and within five feet of the caster. It can do this because instantaneous does not mean the duration of the spell is no time, it means that the duration is less than the time required to cast dispel magic. To argue that gravity fissure cannot damage a target twice because it is instantaneous is to argue that lightning lure cannot damage a target that starts more than five feet away.
So, if it is not because the spell duration is instantaneous, why does gravity fissure not damage a target twice?
Suppose you start your turn within ten feet of the line but not in the area of the line itself, and then fail your save. The second part of the spell says the consequences of this are that you (emphasis mine):
take 8d8 force damage and [are] pulled toward the line until the creature is in its area
Note that it does not say that you are pulled toward the line until you are where the line was. Instead, it says that a failed save results in you being in the area of the line. Since you are within the area of the line while the line is still active, you could then trigger the first part of the spell which says (emphasis mine):
Each creature in that line must make a Constitution saving throw, taking 8d8 force damage on a failed save, or half as much damage on a successful one.
The problem here is that gravity fissure does not conform to how spells in 5e usually work.
Many area-of-effect spells are instantaneous, and their description simply states that damage is done to those within their area:
Thunderwave: Each creature in a 15-foot cube
Snilloc's Snowball Swarm: Each creature in a 5-foot-radius sphere
Fireball: Each creature in a 20-foot-radius sphere
Ice Storm: Each creature in the cylinder
Cone of Cold: Each creature in a 60-foot cone
They don't need to specify what happens when you enter the area of effect because their instantaneous nature means that the spell itself will not be interrupted by movement.
Other, non-instantaneous, area-of-effect spells persist, and thus have to explain when you take damage:
Moonbeam, Sleet Storm, Evard's Black Tentacles, and Cloudkill, for example, all say "When a creature enters the spell's area for the first time on a turn or starts its turn there..."
As stated before, the closest analog to gravity fissure that we have is the instantaneous lightning lure, which both moves a target and then damages it. However, gravity fissure is more complicated in that it has two damage zones and can move targets between them. It thus naturally gives rise to the OP's question of whether the target can be damaged in the outer zone, moved to the inner zone, and then take damage again.
Persistent area-of-effect damaging spells all specify that a target takes damage when it enters them. Even lightning lure, an instantaneous spell, specifies that the target is moved and "then take[s] 1d8 lightning damage if it is within 5 feet of you," with the 'then' signifying that the damage is done when it crosses the point of proximity. Gravity fissure, on the other hand, only says that the damage from the near zone is done to "each creature in that line", presumably meaning at the time the spell is cast. Because it moves creatures between its damage zones, but does not specify what happens upon entry to the inner zone, we can conclude that it does not, in fact, damage the same creature twice.