Just curious is it a one story or two. The other thing I forgot to mention is you Need down weight to pin the wall to the footer to begin with. If the house is jacked up and the ground is wet you run a big risk of the foundation now being a retaining wall to hold back the dirt pressure. Just a FYI
The house post will be the first attack. There you will need to brace on either side to remove steel post to lower its foot print
Since there is brick veneer it could also be a 10" wall then 6" block right below grade which allows the brick ledge.
Just to let you know How I get my information, I started out as a professional Mason ( 30 + ) years and a G.C. For 25 years
I don't normally post that but its hard enough to find a real mason let alone an old school Contractor. Luckily this site has some good tradesmen and not reading answers out of a book. And or have done the research as well as doing the trades
You are in good shape here since its a newer house from the 40s. Most of the underpinning we do is on houses built in the 1800/1900s that are basically dry laid stone at this point with No footers.
Since you have a block wall with a footer you essentially have a concrete footer that becomes a concrete lintel once the dirt is removed to tooth it. Just for FYI because of it being block you can do bigger sections to underpin.
Heres how that works. Look above the area you want to dig out. That last full block becomes the "Keystone" to the imaginable arch. Just look at the head and bed joints and trace that down like a pair of steps snd this id Exactly where the weight transfer will end up.
The pure science for an arch to fail can only happen 3 ways. The "keystone: crushes and fails. The bottom ends of the arch horizontally kicks out, Or the arch all falls in or out. The Romans got it right.
Just on a side note, The masonry trowel is one of the oldest hand tools used on a daily basis and hasn't really changed since the Romans invented it.