How to reset MMR to escape Bronze tier (bottom 1%)?

Ranked and quick play MMR is separate. The only way to truly reset your MMR is to buy the game again on a new account, which will set your MMR to be whatever the average rank is.

However, I strongly advise against doing this. If you dropped down to 700 SR, chances are you probably belong somewhere around that level, plus or minus a couple hundred SR. (Not trying to be rude, just stating how the system is supposed to work.) It might be tough, but if your actual skill level is higher than that, you should eventually climb out on your own. Buying a new account risks you paying extra money just to go through the exact same frustration when you drop lower again.

At the start of every new season, there is a soft-reset of all player's ranks (normalized to the average player rank, which I think is somewhere in silver or gold). I don't know if this also affects MMR, but it should give you a chance to place higher than you might have gotten in the previous season.

Loss streaks happen, and the matchmaking system realizes this. Chances are your MMR is probably not all that heavily affected. You're probably still playing with people of a similar skill level as before, but because your visible rank is lower, you focus more on how "bad" your teammates are now as opposed to how they played before the loss streak.

Even if your MMR is lower now... that's how it's supposed to work. The matchmaking system tries to even everyone out to an approximately 50% win/loss ratio. Trying to get around this system is just asking for frustration.

Your best option is to find some players who are also stuck in the bottom ranks, and group up with them. Find people with mics so you can coordinate your attacks/defense over Discord or in-game voice chat. Even if they are not very good, having consistent teammates and even a small amount of coordination should easily get you all back into the 1000's.

Why is having a group so important? In Overwatch (and many other team-based games), the ranks at the bottom 1%(-ish) are known as MMR Hell - the skills of players varies so wildly, you're just as likely to get a troll teammate who's trying to lose, or a 5-year-old mashing on the controller, as you are a decent teammate.

People claim "over enough games it will even out", but they're forgetting that people often group up, which screws up the balance. Eg. if there's a group of 5 and you're solo-queueing, you have a 1/7 chance of being on their team, and 6/7 chance of being against them. And given that they're likely not deliberately grouping with trolls/5-year-olds, you have a much higher chance of losing.

Thus, getting out of the lowest ranks by yourself takes significantly more effort than at higher ranks, no matter how good you are (and unlike many other team-games, in Overwatch even the best players can't carry an entire team by themselves). Because of this, "playing a lot of games" is not a good option. You will eventually get out of MMR Hell, but depending on your luck it could take a long time.

Placement matches are not a fresh start, they're based off your final placement in the previous season. There is no way to "reset MMR", your only chance is to win more games than you lose.