It was a very unlikely event – when you think of what each side wanted out of annexation, the US wanted the use of Pearl Harbor: they already had it through the reciprocity treaty, which was still in effect. Hawaiʻi sugar growers wanted an end to tariffs on their sugar: they already had it because of the Wilson-Gorman Tariff, which cancelled the effect of the harmful (for sugar) McKinley Tariff. Add to this that it was done illegally through a joint resolution and annexation looks unlikely indeed. When people say annexation was “inevitable,” that might be true in the long term, but at the time it happened, annexation was definitely unlikely.
It may never have happened without a mechanical failure on a ship in Havana Harbor, Cuba – Hawaiʻi was swept, again illegally because of its declared neutrality, into the Spanish-American War. And this war was used as a justification for violating Hawaiʻi’s neutrality and using it as a coaling station for ships on the way to the Philippine front.
The purpose of annexation was gone before it happened – hostilities in the Spanish American War (the purpose of annexation) ended the day before the annexation ceremony in August, 1898! US military personnel camped at what they called Camp McKinley and we call Kapiʻolani Park, sat there for months, seeing no action because the action was over.
It may never have happened if Queen Emma had won the election of 1874 – going back further, Emma’s pro-British attitude may have prevented a reciprocity treaty for sugar, which would in turn have reduced American influence in Hawaiʻi, which itself would have reduced pressure for annexation – we may well have had British accents!
Annexation was done illegally because American Senators opposed it – it bears remembering that the treaty of annexation failed in the US Senate (and only the Senate votes on treaties) because enough US Senators opposed, in the words of one member of Congress, “bringing Hawaiʻi into this complication.” It was not a majority that opposed it, but in order to ratify a treaty, the Senate needed two-thirds of its members to approve, and this they did not do.