What is cheap these days?
Low quality steel is very cheap but also really heavy. You can get a whole crappy bike for a couple hundred bucks. Higher end steel isn't as cheap but is still relatively heavy (compared to aluminum or carbon). You can get this kind of bike in the $1000-2000 price range (e.g. Surly). Aluminum bikes tend to be inexpensive, but also not the lightest. These can also be priced at $1000-2000 (Specialized, Trek, Giant, ...). Carbon comes in a range of prices with various tradeoffs. You can get very budget carbon frames at like $1500 (Winspace) or whole bikes at like $3000 (Giant) (maybe $2000 in non-major brands, very discounted during current market conditions).
For titanium, I'm seeing Black Friday deals starting at like, $3200-3500 (Lynskey / Litespeed). But they're often sold at higher prices than carbon bikes. (For my money, I prefer carbon frames -- you get more flexibility in tube shapes and the end result can be lighter and stronger than titanium.)
Check these out https://www.rodbikes.com/profiles/profiles.php?tag=ultra-lig... steel bikes ~13.5 lbs.
Prices shot up during the pandemic and never really went back down. You're lucky to find a good carbon bike for under $4K these days where you used to be able to find them for $2K.
Everyone's in oversupply now, inventory is listed at steep discounts to 2022-2023 prices.
This bike isn't even on sale and it's under $4k and not a bad bike: https://www.giant-bicycles.com/us/tcr-advanced-2-pc-2025