My first comment here. Hope my answer will suffice!

Yes, there was strong local desire for such a state before the First World War. Yugoslavism became a distinguished segment of the wider Pan-Slavic movement around the 17th century. It was popularised by the Illyrian movement in the 19th century and afterwards, throughout the territories populated by South Slavs, the idea of Yugoslavism was growing strong, helped by the general dissatisfaction with the Austro-Hungarian government.

In Croatia, the Serbs and Croats who lived under Austro-Hungarian thrall were often grouped together as they considered one another to be cast in the same mold. In the early 20th century, these stances were most explicitly espoused by the disciples of Svetozar Pribićević, the leader of the Serb Independent Party (Serbo-Croatian: Srpska samostalna stranka) who advocated for the creation of a Yugoslav state, thus welcoming collaboration with Croatian politicians, which resulted in the SIP merging into the Croat-Serb Coalition. The joint interests and friendship between the two parties culminated in 1905 when two documents were signed - the Rijeka Resolution and the Zadar Resolution, which both proclaimed solidarity and equality between the Croats and the Serbs. On the other hand, the Croatian Party of Rights, led by the likes of Ante Starčević and Josip Frank, opposed the idea of Yugoslavism with zeal.

In the Condominium of Bosnia and Herzegovina, following the Bosnian Crisis, the locals were very much dissatisfied with Béni Kállay's administration, and the Bosnian intelligentsia rallied behind pan-Serbian and anti-Austrian publications like The Bosnian Vila and Zora (Dawn), which helped preserve Serbian national identity. Such a sentiment was supported by many eminent authors, politicians and poets of the time, with the poet and politician Osman Đikić, a Serb Muslim, being an example. This was the ideological basis of the Young Bosnia organisation, frequented by many young intellectuals of the time, an organisation now famous primarily for assassinating Archduke Franz Ferdinand.

In the independent Kingdom of Serbia, the Yugoslav nationalists were influenced by the Risorgimento (Italian unification) and considered Serbia to be responsible of emulating the Kingdom of Piedmont by uniting all South Slavs into one state henceforth known as Yugoslavia. Slovene nationalists like Anton Korošec espoused pro-unification ideas, believing the unification to be a means of freeing Slovenia from Austro-Hungarian control. How deeply ingrained the idea of Yugoslavism was within the nationalist sentience of the time is best exemplified by this Gavrilo Princip quote: 'I am a Yugoslav nationalist, aiming for the unification of all Yugoslavs, and I do not care what form of state, but it must be free from Austria.'

So, that said, the idea was rooted within the collective conscious of a majority of South Slavs of the era, but after the Great War, Yugoslavia wasn't immediately formed. The Corfu Declaration made the Serbian pro-unification intentions rather clear, and once the war ended the Kingdom of Serbia merged with the State of Slovenes, Croats and Serbs, and once the pro-Serbian Whites have outnumbered the pro-independence Greens in the Podgorica Assembly, so did Serbia merge with the Kingdom of Montenegro thus creating the Kingdom of Serbs, Croats and Slovenes, separated into nine banovinas. The newly-formed state was no stranger to separatist and nationalist turmoil, which is why King Aleksandar I changed the name of the country to Yugoslavia in 1929, and started working on eradicating the national identities of Yugoslav peoples from existence for the sake of creating a unified state, not separated by neither religion nor ethnicity. This process was later continued by the communists but has evidently failed to take hold, as shortly after Tito's death, Yugoslavia again found itself divided by separatism and nationalism promoted by all the parties involved in the conflict.

Sources:

V. Ćorović - Istorija Srba

J. R. Lampe - Yugoslavia as History: Twice There Was a Country

Z. Pavlović & J. Bosnić - Mozaik prošlosti

Lj. Antić - Prvi svjetski rat i Hrvati