Who is the first acharya of the Sri Sampradaya?
According to the Vedic lineage of Śrī Sampradāya as mentioned below:—
इममेव मनुं पूर्व साकेतपतिर्मामवोचत् अहं हनुमते मम प्रियाय प्रियतराय । स वेद वेदिने ब्रह्मणे स वशिष्ठाय स पराशराय । स व्यासाय । स शुकाय इत्येषोपनिषत् । इत्येषाग्रह्मविद्या ।
Here Śrimati Sītā Maharani is telling that she got Mantra from Saket Pati Śrī Rāma after than she passed it to his beloved bhakt Śrī Hanuman after that Sri Hanuman ji passed it to Brahmā ji from Brahmā ji to Vashistha Ji from Vashistha Ji to Parāshara Ji from Parāshara Ji to Ved-Vyäsa Ji and than to Shukacharya Ji.
(Atharvavedā Maithili Maha Upanishad)
Śrīmati Sītā Maharāni is the first Ācharyā of Śrī Sampradāya.