Not to dissuade anyone else from answering her specifically, but this is a question you might want to ask in r/linguistics, as this question strictly speaking falls more under linguistics than history, per se. Here we can try and answer the question when did people start referring to ships as

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Using she to refer to ships is not just for vehicles anymore! You see it used with vehicles (e.g. in the song 12 Days on the Road by Dave Dudley), but with natural phenomena, rooms, musical instruments, clothes, food and drink, the list goes on and on (Hornoiu 2009).

Let's focus on ships, however. There is a pretty long tradition of referring to vehicles in English (let's focus on that for now) with a feminine pronoun. This is interesting, as grammatical gender has almost completely disappeared in English. I'm not entirely sure where this tradition came from, but it's clear that it already existed in English by the 17th century: in Ben Johnson's 1640 grammar of English, he explicitly says that ships should be refer to with she rather than it (even if the ships are named after a man!). With regards to countries, it's not impossible that it's based on analogy (similarity) with French, wherein the majority of (European) country names are feminine, but I don't have any conclusive evidence to prove such a connection.

But to answer the question why I'm going to follow Janet Duke's discussion in her book The Development of Grammatical Gender, in which she focuses on six Germanic languages. She points out that the usage of animate (living) pronouns he and she has mostly do with either personification and sexualization (Duke 2009: 226-7). To make this a bit more clear: we tend to say "he" or "she" to things that we feel particularly close to, and this doesn't always depend on whether the thing is alive or not. In the case of vehicles, it seems that it mostly has to do with a sense of closeness – or possessiveness (depending on your interpretation) – to the object. There is so much more that could be said about this subject – including when the first usage of referring to a ship with "she" comes from – but that's a very short answer to why we do this.

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Corbett, G. (1991). Gender (particularly pages 180-81)
Duke, J. (2009). The Development of Gender as a Grammatical Category: Five Case Studies from the Germanic Languages
Hornoiu, I. (2009). "The Category of Gender in Present-Day English".