In this paper, we raised the question of whether initial cosmological singularity can be proven by cosmological tests. The classical general relativity theory predicts the existence of singularity in the past if only some energy conditions are satisfied. On the other hand, the latest quantum gravity applications to cosmology suggest the possibility of avoiding the singularity and replacing it with a bounce. Bounce is the moment in the evolution of the Universe when the Universe’s size is minimum. Therefore the existence of observationally detected bounce in the Universe’s past could indicate the validity of the loop quantum gravity hypothesis and nonexistence of initial singularity which is present in the classical \LambdaCDM. We investigated the bouncing model described by the generalized Friedmann-Robertson-Walker equation in the context of the observations of the currently accelerating universe. The distant type Ia supernovae data are used to constrain the bouncing evolutional scenario where the square of the Hubble function is given by the formula , where are density parameters and n > m > 0. In this paper are shown that, on the basis of the SNIa data, standard bouncing models can be ruled out at the confidence level. After adding the cosmological constant to the standard bouncing model (the extended bouncing model), we obtained as the best fit that the parameter is equal to zero which means that the SNIa data do not support the bouncing term in the model. The bouncing term is statistically insignificant on the present epoch. We also demonstrated that BBN offers the possibility of obtaining stringent constraints of the extra term . The other observational test methods like CMB and the age of oldest objects in the Universe are also used. We use as well the Akaike informative criterion to select a model which best fits data and we concluded that the bouncing term should be ruled out by Occam’s razor, which makes the big-bang scenario more favorable than the bouncing scenario.