I think that's a matter of opinion. The term Empire is simply "an extensive group of states or countries under a single supreme authority." That seems to be the case from day 1 when it comes to the Ottomans. The states and principalities of Greeks, Bulgarians, Assyrians, and Armenians were conquered and governed. But let's not forget that the Ottoman dynasty was merely just another Turkic state in Anatolia. So if you're asking for my opinion, I think the notion of Empire came when the Ottomans managed to subdue rival Turkish principalities such as the Karamanids, Karesi, Germiyan, Aydin, etc. etc. So after its conquest of those rival Turkish principalities, it became the dominant force in the region and thus an Empire by definition. The European states may have not considered it as such though up until Selim's and Suleyman's conquests. But that shouldn't matter.

Empire is an exonym. It's a Latin term commonly used in Western languages in various contexts. Here it simply serves to denominate a non-western monarchy, v.g. Empire of Japan, China, Ethiopia, etc. Internally, the Ottomans never proclaimed to be an Empire, that's a Western terminology, the Ottoman Sultans used different terminologies related to their own culture(s) to title themselves, e.g. Khan of Khans (Turkic-Mongol); Sultan of Sultans (Arab-Muslim); Shah of Shahs (Persian); etc. As far as I know, the common name for the Ottoman Empire was, simply, the Ottoman State.