One time I had a dead battery on my astrovan, it wouldn't crank over. I had one of those 18ah agm jump starter but it was also dead at around 12 volts, it wouldnt crank over the van, but I left it connected for about 1/2 hour while I decided what I was going to do. I decided to crank the van over one last time, and it crank slowly but it started. The agm jumpstart put just enough amps to give me one crank.
In an emergency, I think your bluetti can put enough amps into your battery to start it, but it might take 1/2 an hour. But to improve your chances you can always build a boost/buck converter to turn the 12.6 volts from the bluetti into 14.4 volts to give the start battery a quicker boost. On my van I use a boost/buck converter to top off my start battery from the house battery every day. No need to buy a jumpstarter unless you need the engine to start right away.
This boost/buck converter will turn 12 volts into 14.4 volts at 6 amps, and will give your lead acid a quick boost.
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There have been times when my start battery was completely dead and it wouldnt jumpstart and have also encounter situations where I tried to jumpstart someone with jumper cables and there car wouldn't start because the battery was completely dead. Thats one reason I don't even carry a jump pack anymore. I carry jumper cables and I also carry a small oddysey 16ah agm, that I can use to jumpstart my van or if the battery is completely dead I can just use the oddesey as a start battery it has the side/top posts, the oddysey is a beast of a battery for its size.
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