And the answer to the question, can you detect a start bit, is, you always can't if the data stream is continuous,
You are talking about a UART being wired into an existing ongoing non-stop stream. Yes, such a hookup will potentially continuously mess up the receiver until there is a large enough break in the source data.
Yes, exactly, you got it

. Such a hookup is the easiest way to demonstrate the problem, but even if you specify a certain power-up sequence, so that one supposedly does not wire "into an existing" stream, the problem goes nowhere, as any loss of synchronization for whatever reason (SI, EMI, bug, etc.) causes the problem again. So it's not a robust system.
Adding idle periods (I personally use something like 10 bit times long, or slightly more) to force resynchronization every now and then is an actual solution to the actual problem and will limit the duration of the failure. If the system has some kind of packetized nature, then the obvious synchronization point is between the packets.
The attitude of blaming others when you have designed a flaky system which fails until power-off from any single communication failure is a BS attitude. And to design your own UART? What now, design your own USB-UART adapters and sell them with your system, and forbid using other brands of adapters in the user manual? Sounds like a massive case of Not Invented Here, and why? Just because you don't need to admit not knowing about a thing

. Maybe just adapt the idle period resyncs instead, like everybody else does, and don't reinvent the wheel.
There are two types of people: those who can admit they did not know something, and
enjoy the feeling of learning a new thing, and improve as engineers. And then there are those who go in defensive mode because they fear admitting they did not know it shows a weakness. This becomes a problem when they go to such great technical lengths as redesigning standard parts just to avoid admitting the mistake. This also explains why some products have a weird legacy and are PITA to deal with because of strange, non-standard conventions and requirements. Weird power sequencing requirements for no apparent reason easily cost days of development time at customer, and extra components, too, so they are generally frowned upon, and as a designer I rather choose a component with no such extra pain.