You just need to "make it so" and set a time and ignore the issue of believability
At this site I found the following reference:
I've had some experience with drilling hard rock on Canadian Shield granite with a Gardner Denver 800 cfm (200 hp) compressor and drill rig using a 3 inch bit. We would generally be able to drill 300 feet in 8 hours using percussion. Percussion is somewhat like using a pick.
200 hp gives us 300 feet x 12 inches x 3.14 x 3 inches squared / 4 = 25,434 cu. inches chewed up in eight hours. ... Now I know that an athlete can put out 0.25 hp for short durations. At this point I'll assume that you can put out something somewhat less, lets say 0.1 horsepower for 6 hours.
Therefore I'm figuring you might chip out 9 to 10 cubic inches.
Now, you tell us nothing about the tunnel other than the length. So, some assumptions:
We need to be 100% in bedrock because there is no tech in the 1450s short of magic that can hold up an ocean.
The tunnel would need to be enormous to carry air through that length of tunnel (it's probably still unrealistic, but let's roll with it). Let's say at least 30' in diameter.
The average depth of the ocean is 12,100 feet with depths to 36,200 feet. Let's just assume the average and assume you're 100 feet into bedrock to guarantee the ceiling stays up (I'm going to simply assume nothing leaks. That's a falshood so magnificent that the devil laughs and angels weep, but we'll assume it). So, you need to dig down from the beach, 12,230 feet, then across 700 miles, then up again another 12,230 feet.
At 10 cubic inches per person per day
You could have about, oh, 20 people actually working the rock face with ladders. Even if you're working from both sides at once (a miraculous feat of engineering in the 1450s), you're hauling the debris back 350 miles and lifting it 12,000+ feet. (You know you'll be creating mountains with the tailings piles, right?)
So, 20*10 = 200 cubic inches a day (we'll ignore the cottage industry keeping the wheel barrows and picks in supply) or 0.1157 cubic feet a day. The volume of a cylinder is easily found online, so you need to remove 2629838205.89 cubic feet.
22,729,802,989.58 days | 62,273,432.85 years
Read that slowly... 62.3 million years
OK, that was dramatic, but the rating was for only 6 hours of work. So we need to divide it by 4.
15.6 million years.
OK, ignore the engineering miracle, we're working from both sides...
7.8 million years.
How many people?
I know some modern miners who can work all day — but they're not swinging picks, they're handling drills. You'll be swaping out guys every 2 hours. Maybe they can swap back in. Let's say you can do this 3 times in a day. That's 4 teams. 40 people.
But at the end you need to move tailings 350 miles (at best, wo and we're breaking rock 24/7. Your average wheelbarrow can carry about 4,000 cubic inches (this is a guess-an-average based on looking at a few wheel barrows online). So you're moving one wheel barrow every fortnight — but that guy won't be back for a while.
Your average walking speed is 3.1 miles per hour. Our workers are in great shape, but they're pushing a wheel barrow. Let's say 3 mph. 350/3 = 116.67 hours or a round number of 5 days to walk out.
At 10 hours per day we're talking 12 days to get out. That's almost as unbelievable as the 7.8 million year number, but let's roll with it.
This guy can't quite get back in time for the next load, so you need 2 dudes working the wheel barrows. Someone to cook at every 1/2 day point (24 dudes), someone to move water and food (2 more dudes), we're feeding the 40-person crew, 8 more dudes, and who knows how many are supporting on the outside. I'm going to ignore clothes, repair, etc. (I'm ignoring an unbelievable number of details... weeping angels...)
Oh, let's round it up to 100. On each side. So 200 dudes.
The problem is you can't get more on the rock face, and that's the tall pole in the tent.
7.8 million years...
Start at 15, end at 55: 200 dudes for 40 years. 195,000 generations...
39 million people. Excluding the babies, wives, old folks, and everyone supporting the 200 dudes.
Is this at all believable?
Is this at all useful?
Nope. Your tunnels were built by magic or using equipment a whole lot more powerful than picks.
Before you jump to explosives...
You need to understand air blasts. I used to live in Idaho's Silver Valley, where there are many mines and a lot of graves holding the bodies of miners killed via air blasts. You're inside an entirely inflexible tunnel. The force of blasting must go somewhere. Where it goes is through the heads of your miners all the way back to the tunnel entrance.
This means vacating the tunnels whenever you blast. but blasting will only convert cubic inches to cubic feet. It's not going to bring the time down to centuries. You'd be lucky if it brought the time down to 100,000 years.
And you'd no longer be able to do it with just 200 people (39 million over the span). You'd need thousands. (Probably still 39 million, just over the shorter span.)
For one 700 mile long tunnel