Language and its grammar develop over time. It's not something that is invented or started suddenly.
But in the case of Sanskrit, you can say that Panini is a father of Sanskrit grammar due to his fabulous work towards standardizing Sanskrit grammar through his text Ashtadhyayi - अष्टाध्यायी (book based on grammar).
Panini wasn't the first grammarian of the Sanskrit language. In fact, in his book he mentioned some grammarian's names like Galav, Shakatayan, Shakalya, etc. which existed before him, and did some work on Sanskrit grammar.
But Panini's Ashtadhyayi is considered a very thourough and complete work in terms of grammar. Panini is considered as a “first descriptive linguist” and “father of linguistics” too. Panini was an ancient Sanskrit philologist, grammarian in India.
The other famed grammarians who influenced the Sanskrit language and helped standardize it are, Patanjali (Mahabhashya), Bhartuhari (Vakyapadiya), Katyayan (Vaartika), Pingal (Chandashastra), Yaska (Nirukta), Vararuchi (Vakya Panchadhyayi), etc.
Language and its grammar develop over time. It's not something that is invented or started suddenly.