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An early analysis of growth dynamics for infectious diseases, like COVID-19, is needed to dissect the crucial driving factors that result in rapid disease transmission, refine the measures taken to control the pandemic and improve disease forecast. The phenomenological models are used to identify the initial climbing growth period of COVID-19 outbreak in India and have modelled 3 major epidemic growth models: Generalized logistic growth, Logistic growth and Generalized growth, to predict the growth in the total number of positive cases, daily increase in the number of positive tested cases and the daily growth rate in confirmed positive cases, dated from Apr 10, 2020, to Apr 20, 2020. The bootstrap resampling method is applied for data prediction to process the sample data, dated from Jan 31, 2020, to Apr 10, 2020, and to calculate the 3 major growth parameters: r (Rate of growth at an early stage), K (Final epidemic size) and C(Number of aggregate cases at time t), which are used to calculate confidence intervals which predict the future direction of the curve and increase in the number of confirmed cases with 95% accuracy for the interval Apr 10, 2020, to Apr 20, 2020. Our models predict exponential and sub-exponential spread rate in the number of positive cases in India from Apr 10, 2020, to Apr 20, 2020. Our findings reveal that significant measures are needed to control the transmission rate of the virus in the community, as the models predict sub-exponential growth in India.