I'm personally a big fan of the optical telegraph, which did get some limited use, but not nearly as much as it could have. Once you have the ability to make telescopes on a decent scale, it's pretty easy to set up a network. So really any time from about 1610 onwards, it's feasible, and Robert Hooke did propose a system in 1684 (albeit one quite different from the systems that were actually used).
France's network is probably the best known, using semaphore, but this system seemed to have a lot of disadvantages. I'm much more of a fan of the Edelcrantz system of shutters (which is not dissimilar from the Murray system that the British Admiralty used around the turn of the 19th century) that Sweden had, as it was much faster, and could be used at night as well.
The Murray system used in Britain was able to get a message from London to Portsmouth in about 7.5 minutes, which is about 10 miles a minute (so 600 miles an hour). I've seen claims that they were able to get a message to Deal from London in just a minute, which suggests a speed of about 4800 miles an hour (which absolutely will not be feasible over long distances). The systems of OTL were used pretty much exclusively for military communication, which is how I'd expect such systems to originate, but if they can successfully be shown to have a civilian purpose, I see no reason why they couldn't become more widespread. Assuming an Edelcrantz-esque system, you've got 10 bits, and therefore 1024 combinations to work with. So alongside pure letters, numbers, symbols, and control codes, one can fit in a lot of shortened words and phrases to speed up communication.
Granted, the system does have drawbacks. Long-scale travel (i.e. from one side of the country to the other) would require "stopping points" to decode the message and clean it up (i.e. remove any backspace or other similar control codes) and for routing (though this isn't actually all that different from an electrical telegraph, and I suspect that an electrical telegraph would end up repurposing the optical stations). Poor visibility can completely shut down the system, and if you're not using the incredibly smart Edelcrantz system (which illuminated the shutters and used the complements of the code), you can't use them at night either. Also, you can see the messages being transmitted (though this might lead to some early advanced cryptographic efforts), so pay off the operators of one station and you can hijack the network (the Blanc brothers did this with the French network), though making the system available for civilian use will reduce this considerable (though privacy may still be an issue).
Also, it's not really possible to have a system work over bodies of water, as can be done with an electrical telegraph. No equivalent to underwater cables (not unless you've got some really dedicated workers).
But I can absolutely see a world where the optical telegraph becomes a much wider success earlier, which could quite easily spur on the development of cryptography (early adoption of polyalphabetic cyphers?), which in turn could encourage the development of mechanical computation. And as already said, when the electrical telegraph is developed, you've already got a lot of the infrastructure set up, and I could absolutely see a hybrid system being used for a time (wherein high priority messages are done by electrical telegraph, and less important ones use the optical system, but I'm just spitballing at this point).