If the Borg possess the ability to time travel as we have seen, why would they travel in space to their target (i.e. Earth) then back in time, could not they do it from the Delta quadrant? That is move back in time in the delta quadrant and then travel to any planet to assimilate. No combat, battles or anything. Or would that create paradoxes?
From 1429, she gained the time travel technology that she utilized aboard the Borg sphere that traveled back in time; however, the device malfunctioned - where she had set it to take her only a few days in the past, it returned her several centuries. After this, the Queen decided that she would only utilize it in an extreme emergency, as to prevent further malfunctions.
The movie First Contact opens with a battle against a Borg Cube, which is destroyed. The Sphere detaches and goes back in time as a last-ditch effort as the Cube is destroyed. This (non-canon) quote provides a possible reason - although it's not clear whether or not the sphere that Memory Beta refers to is the one from First Contact, or another one the Queen was testing the technology on.
A couple days may well have been the intent of the Sphere from First Contact; it could have contacted the Cube before it was destroyed and altered the outcome, without major changes to the timeline, which wouldn't necessarily have been a desired outcome for the Borg considering the numerous conflicts they've already had.
(Aside, preventing humans from reaching space before the Federation was created would have been quite a bad mistake on the Borg's part, since their conflict with Species 8472 would likely have already started by that time (Scorpion takes place on Stardate 50984.3, and First Contact on Stardate 50893.5). If there was overlap between Voyager's assistance and First Contact, their primary goal would've been to destroy the Federation after Voyager arrived in the Delta Quadrant. This also would explain why the Borg in Regeneration didn't stay on Earth and try to assimilate the planet...)
The Borg are both patient and logical. They are also cautious. Time travel is dangerous - you run many risks in attempting it. You could change things to make the future significantly worse for you.
Consider the Borg that visited the past - they were in a single Borg Sphere. There were very few drones and the Borg Queen. The humans on the planet were recovering from a war. They had weapons aplenty, and were not shy about using them - they'd had plenty of practice.
Eventually, to conquer the planet, the Borg would have to land and/or transport. This opens them up to the chance of violence. The humans were well-versed in firearms, and could have killed drones by the dozens. There's also a strong chance that the humans could piggyback on a Borg teleport to get back to the ship. The chances are low, but there. And with armed humans on the ship, the Queen would be vulnerable.
Time travel was the Borg's backup plan. They didn't really want to go back in time and have two Collectives - one in Delta and one in Alpha. They had strong reasons to believe that the Cube would reach Earth, and could easily have begun assimilating Earth without time travel had they succeeded (which, mind you, they very nearly did). The Sphere was their backup plan, in case something stopped their Cube.
One could expect that this is a standard methodology for the Borg when confronting a species with technology that makes Borg defeat possible. First, try for an outright military victory. In the event that it fails, send in a second Cube some time later - the second Cube could smash defenses that had been crippled by the first, and have a time-travelling Sphere ready in the event of the second Cube's destruction.
It is obviously in the Borg's best interest to assimilate a species at the latest possible point - each species brings unique technical and/or cultural capabilities. Assimilating Earth in the late 2000s would not gain the Borg access to any of Starfleet's advanced technologies, some of which could have been useful to the Borg.
All of the above answers are good, but I want to add one more factor: the Federation's pre-existing infrastructure.
The Borg were able to rapidly assimilate the Enterprise-E because it functioned on equivalent technology. But imagine the Borg trying to assimilate us now, or during World War II, or during the Roman Empire. They've got no technology to work with, no tech to assimilate or pieces to use. They'd be starting from scratch, with a whole planet in front of them. At a certain point, they wouldn't even be able to "assimilate," they'd just have to straight-up "build."
Not only would it be not worth the investment (since the Borg famously only assimilate tech that will help them improve), but it would also be a HUGE pain. Imagine an assimilated Renaissance Earth: millions of Borg drones, but a planet of wood and stone. Anything before the late 20th century and they'd barely even have very much metal to re-forge. They would have to build mines just to extract the iron from the ground, so they could start building charging stations and ships.
Much better to assimilate the Federation as-is, with its huge population and powerful "modern" (for the future) infrastructure that can quickly be repurposed for the Borg's needs, and switch to time travel only when necessary.
There's no prize in assimilating Earth in the past.
Borg are driven to assimilate species only if they can add to the collective.
Humans are biologically inferior to species that the Borg have already assimilated.
The Borg are more interested in the Federation's technology.
Traveling back in time to assimilate pre-warp Earth would gain them nothing but a biologically unremarkable species with no redundant vital organs, etc.
What the Borg ought to do instead is send more than one ship to assimilate Earth.
We've heard about he Borg assimilating other Delta Quadrant species (like the one in VOY "Hope and Fear".) He spoke of 'hundreds of cubes' when the Borg finally got his species.
Both times the Borg launched an attack on Earth, it was just a single vessel that juuuuust about succeeded.
Sending two ships would be a better idea. Or three. Or fifteen.
Well, if we are to believe the later events in Voyager, then Borg ships needs transwarp conduits to travel very large distance at very high speeds. It is shown many times, so the Borg make significant technical progress (through assimilation) over the course of centuries. The transwarp network is a relatively recent addition, definitely less than three centuries old. So these transwarp conduits don't exist in the past, and traveling through time and then through space to get to past Earth is not an option.