Firefighter here. I'm on mobile so I'll add sources when I get to a PC. (2300 eastern time give or take) Bear with me mods.
Up through about the 60s there was no real airpacks,* and they weren't really in common use until the 80s or 90s because of a "those things are for pussies" mentality. (We still have a guy that hangs out and makes fun of us for using them. He was in WWII, & the toxic fire of 78, and is under the assumption that since he's fine, it makes you healthier.)
So "did they just not go into burning buildings?"
They absolutely went in. There's 2 things to consider though. First is that they couldn't get as deep into the job as we can today, and in going in they have to be literally "sucking the carpet" when it was rocking. This was taught as a legitimate tactic: put your face on the ground, and take a breath through the rug, using the fibers as a filter. (This is heavily documented in the book "Engine Co. 82" documenting the war years on an FDNY engine)
I don't know that I'll be able to find documentation on this one (and if I can't I'll amend it) but another tactic was to just smoke. There was a mentality that a cigar or big cigarette was "clean smoke" and wouldn't hurt you as much as job smoke.
The second thing to consider is that fires then were not the same as today's fires. Today we deal with a lot more lightweight construction, and many many many more synthetics than they did 100 years ago. (I'll add a video demonstrating this when I get to the PC, it's a pretty profound difference) The days of old, you were dealing with wood, & natural fibers mostly. This led to less thick smoke, less volume of smoke, and slower evolution of fire conditions. There was far less risk of a room flashing on toy without warning. Today we're dealing with buildings in which the vast majority of the fire load has some type of synthetic, or petroleum product in them. This means that they burn hotter,and faster, and less completely. This means there is way way more smoke, it's thicker smoke, it's deadlier smoke. The fact that it doesn't burn completely means that the risk of flash or backdraft is orders of magnitude greater. SCBA is an absolute necessity today. You simply are not physically capable of just toughing it out like they did before.
A bit off track, but relevant here. When packs had final stage regulators on the belt, another tactic was to disconnect the hose from the reg, and tick the end of it inside your coat to act as a filter. This was also in textbooks, I promise to cite!
*we carry compressed room air in those packs. Pure O2 + Fire is not a great combo.
I'm sure I missed some bits, and wasn't as clear as possible on others so please ask away! I love talking about the job, and hope everyone learned something!
Edit: Sources: An article Published by PBS Apparently the SCBA goes back as early as WWI, and wasn't actually required until the 1970s.
This one seems to be drawing on the same source as the PBS article
This & This & This Are the types that I mentioned would be tucked into the jacket without actually being connected to the air supply.
This article by PJ Norwood is a quick and interesting (although not in-depth) explanation of why tactics and equipment change. Maybe not the best source, but PJ is very knowledgeable and it's sorta relevant.
THIS article is much more in depth, and details differences between older and newer fires, and why firefighters are cancer ridden. Also check out the section headed "To filter breathe, or not to filter breathe? That is the question" for a mention on sucking the carpet, and tucking the hose into the coat. All around a great article on proper air management in today's fire service.
Link to "A Report from Engine Co. 82" A book I mentioned in the post. It's a great, and very easy read chronicling some of the war years in the Bronx, NYC. They had SCBA at this time, but as I mentioned, it wasn't in vogue to use it.
A Good Job: Stories of the FDNY is an hour long youtube video made and hosted by Steve Buscemi. (Originally of FDNY Engine 55, Little Italy) Great photos of the way they did things back in the day. Absolutely mental guys. Some great videos of more modern work involved as well. I'll point you towards specifically the 29:00 minute mark, describing the war years, including video of crews making a push on a good job without packs. (and the results of these tactics around the 29:30 mark) The 30:00 mark begins the Downey brothers describing what it was like to fight fire with their father, who was as salty as they come.
If nothing else; watch 30:00 to 32:00 for an overview of the advent of SCBA in the FDNY. (Which is a good indicator for trendsetters in the business.) Note: Following that portion, guys begin talking about their first deaths on the job, if you're unable to cope with hearing that, you should skip that part.
I'd also like to add in the source given to us by /u/ArizonaPete