Can the initial singularity be detected by cosmological tests?

In the present paper we raise the question whether initial cosmological singularity can be proved from the cosmological tests. The classical general relativity predict 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 of possibility of avoiding the singularity and replace it with the bounce. The distant type Ia supernovae data are used to constraints on bouncing evolutional scenario where square of the Hubble function $H^2$ is given by formulae $H^2=H^2_0[\Omega_{m,0}(1+z)^{m}-\Omega_{n,0}(1+z)^{n}]$, where $\Omega_{m,0}, \Omega_{n,0}>0$ are density parameters and $n>m>0$. We show that the on the base of the SNIa data standard bouncing models can be ruled out on the $4\sigma$ confidence level. If we add the cosmological constant to the standard bouncing model then we obtain as the best-fit that the parameter $\Omega_{n,0}$ is equal zero which means that the SNIa data do not support the bouncing term in the model. The bounce term is statistically insignificant the present epoch. We also demonstrate that BBN offer the possibility of obtaining stringent constraints of the extra term $\Omega_{n,0}$. The other observational test methods like CMB and the age of oldest objects in the Universe are used. We also use the Akaike informative criterion to select a model according to the goodness of fit and we conclude that this term should be ruled out by Occam's razor, which makes that the big bang is favored rather then bouncing scenario.