Tibet is not listed anywhere as a former member of the UN, even though there is 5 years between the formation of the UN and the PRC's invasion and subsequent annexation of the country.
Did Tibet decide not to join the UN, did it not get around to it (it seems neighbours Nepal and Bhutan joined later), or is there some other reason as to why the country never joined?
Simply put, there was no support for its recognition as an independent and sovereign state.
At the time of the creation of the UN, the P5 Security seats (with veto power over admission) were China, the USSR, the US, France, and the UK. None of the 5 recognised Tibet as independent and importantly, one explicitly claimed Tibet as a part of its territory (China.) In any case, the ROC at the time would've certainly vetoed the admission of Tibet into the UN; I would recommend looking into the case of the ROC veto of Mongolia's admission (the only use of the Chinese veto under the ROC ever) as an example of what likely would've happened. However, in this scenario, unlike Mongolia, which had the support of the USSR and was eventually forcefully admitted because of a USSR threat to stop admission for any newly decolonised African state if Mongolia were not admitted, nobody particularly cared for or supported Tibetan independence.
Additionally, it takes time between application and admission; Nepal applied in 1949 and did not gain admission until 1955 for example.
As to the specific reason why Tibet didn't even send in an application, maybe somebody else can chime in and add context if there are any sources (but I'm doubtful.) The simple reality though is that there was no way Tibet would've ever been admitted even if they had sent in an application.