To put it extremely briefly, the founding of the Republic after winning the War of Independence took so much time, because the Republic was not the initial goal anyway. The goal of the war was to save Turkey from the invasion.

Mustafa Kemal Pasha's (later, Atatürk) rule was by no means uncontested during and immediately after the Turkish War of Independence (1919-23). In the Assembly in Ankara, there was a quite heterogeneous opposition group called 'the Second Group'. The group included individuals from various backgrounds; some were conservatives and Islamists, others liberals of sorts, and so on. What they all agreed on was that Mustafa Kemal's rule had to be limited before he became a dictator. In many minds, the memories of Enver Pasha were still too fresh to let anyone become the strongman. Others were concerned about the rumours about Mustafa Kemal's intentions and lifestyle. Mustafa Kemal did his best to cater to the more conservative circles during the war, often proclaiming allegiance to the Caliphate and Sultanate. But the fact that he was often surrounded by younger intellectuals and politicians known for their radical Westernist ideas (like Falih Rıfkı Atay) did not help in hiding his intentions.

An arguably more dangerous (dangerous from the Kemalist perspective, of course) opposition was emerging from within the Kemalist leadership, however. Many leading generals of the War of Independence were growing dissatisfied with what they perceived as the increasing strongman tendencies of Mustafa Kemal. Some, like Ali Fuat (Cebesoy) seem to have mainly moved to the opposition due to such concerns. Others like Rauf (Orbay) were terrified of the idea that Turkey could do without the Sultanate AND the Caliphate. In other words, they found the Kemalist project simply too radical.

The new opposition was thought to have a sizeable backing in the army, as commanders like Kazım Karabekir and Refet (Bele) among others joined its ranks. The opposition did not formalise by the founding of a new party before 1924; Rauf himself remained the PM until August 1923. But a different development in November 1922 meant Turkey was, in effect, a republic before October 1923.

In what was likely a final 'divide and conquer' attempt, the Allies invited both the Kemalist government in Ankara and the Istanbul government to the London Peace Conference after the Turkish War of Independence. The Kemalists quickly seized the opportunity and had the Assembly in Ankara abolish the Sultanate. To provide a bit of context, the Sultanate and its government in Istanbul constantly avoided confrontation with the Allies during the War of Independence. The government agreed to the Treaty of Sevres in August 1920, which would leave Turkey as a rump state in Central Anatolia. Furthermore, the Istanbul government later denounced the Kemalists as provocateurs and gangs, and then passed a death sentence for leading Kemalists, including Mustafa Kemal, in absentia. All these wrecked its reputation and by the time the Kemalists were ready to abolish the Sultanate, many potential advocates were rendered silent by the Istanbul government's and Sultanate's own actions. However, a member of the Ottoman royal family, Abdülmecid Efendi did remain in Istanbul as the Caliph. A direct attack at the Caliphate seemed too imprudent to the Kemalists at the time; there was even a battle of pamphlets, some advancing the view that Caliphate without Sultanate was unprecedented and meaningless, some claiming it was the original form of Islamic government and acceptable.

With the Sultanate gone, the opposition (including both some Second Group figures like Lütfi Fikri and the 'Pashas' opposition, most prominently Rauf) started gathering around the Caliphate. What exactly the regime in Turkey was was debated heatedly in the Assembly and the press. Mustafa Kemal was criticised for having established a regime that was neither like democracy nor socialism; he replied this was something expected, since 'we [the Turks] resemble ourselves', not any strangers and their political systems. In practice, as before, Turkey was a republic. The Sultan was gone, there was a presidential figure in Mustafa Kemal, and there was a powerful Assembly. But what was the role of the Caliph and what were the relations to be like between him, the Assembly and Mustafa Kemal? These were not clear. Moreover, though the Sultan was gone, the opposition in the Assembly and among the Pashas remained. Clearly, this would not do if the Kemalists were to obtain the power for good and realise their project.

What then happened was, to put it briefly, Mustafa Kemal triggering a parliamentary crisis in an already fragmented Assembly, then claiming new elections were required. In September 1923, he announced the founding of his People's Party (later the Republican People's Party). The Kemalists did not completely dominate the new assembly, there was still opposition within the Party. Yet, the new Assembly was more loyal to Mustafa Kemal and more welcoming towards his circle's radical project. Having set the scene in this way, Mustafa Kemal then proposed that the Republic of Turkey be established. On the 29th of October 1923, the Assembly agreed and Turkey became a Republic. Meanwhile, Karabekir and others complained how such a decision could be made with many of them away and literally all of them kept in the dark.

We do not know if the Kemalists always intended to proclaim a republic. Some scholars go so far as to argue that the proclamation of the Republic was completely conjectural and pragmatic. I think this is a little bit of exaggeration; I agree that the Republic as such was not in the minds of the leading Kemalists in, say, 1921, but the overall nationalist Westernisation project was most likely already a plan for the future. So, I think, it is best to see the proclamation of the Republic as something that was very much in tune with the overall Kemalist project and that was realised in response to a concrete crisis.

Sources:

Ahmet Kuyaş, 'Neden Cumhuriyet', Cogito, 15: Cumhuriyet: Alkışla Olmaz, (Summer, 1998), 114-118.

Mete Tunçay, Türkiye Cumhuriyeti'nde Tek Parti Yönetimi'nin Kurulması (1923-1931) (Ankara: Yurt, 1981).