In the presented paper we raised the question whether initial cosmological singularity can be proved 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 has minimum. Therefore the existence of observationally detected bounce in past of Universe could indicate the validity of the loop quantum gravity hypothesis and nonexistence of initial singularity which is present in the classical ΛCDM. We investigated the bouncing model described by the generalized Friedmann-Robertson-Walker (FRW) equation in the context of the observations of the currently accelerating universe. The distant type Ia supernovae data are used to constraint on bouncing evolutional scenario where square of the Hubble function H 2 is given by formulaewhere Ω m,0 , Ω n,0 > 0 are density parameters and n > m > 0. In this paper are showed that the on the base of the SNIa data standard bouncing models can be ruled out on the 4σ 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 Ω n,0 is equal zero which means that the SNIa data do not support the bouncing term in the model. The bounce term is statistically insignificant on the present epoch. We also demonstrated that BBN offers the possibility of obtaining stringent constraints of the extra term Ω n,0 . 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 fits data the best and we concluded that bouncing term should be ruled out by Occam's razor, which makes the big bang scenario more favorable then the bouncing scenario.