Detection of solar gravity modes remains a major challenge to our understanding of the innerparts of the Sun. Their frequencies would enable the derivation of constraints on the core physical properties while their amplitudes can put severe constraints on the properties of the inner convective region. Our purpose is to determine accurate theoretical amplitudes of solar g modes and estimate the SOHO observation duration for an unambiguous detection. We investigate the stochastic excitation of modes by turbulent convection as well as their damping. Input from a 3D global simulation of the solar convective zone is used for the kinetic turbulent energy spectrum. Damping is computed using a parametric description of the nonlocal time-dependent convection-pulsation interaction. We then provide a theoretical estimation of the intrinsic, as well as apparent, surface velocity. Asymptotic g-mode velocity amplitudes are found to be orders of magnitude higher than previous works. Using a 3D numerical simulation, from the ASH code, we attribute this to the temporal-correlation between the modes and the turbulent eddies which is found to follow a Lorentzian law rather than a Gaussian one as previously used. We also find that damping rates of asymptotic gravity modes are dominated by radiative losses, with a typical life-time of $3 times 10^5$ years for the $ell=1$ mode at $ u=60 mu$Hz. The maximum velocity in the considered frequency range (10-100 $mu$Hz) is obtained for the $ell=1$ mode at $ u=60 mu$Hz and for the $ell=2$ at $ u=100 mu$Hz. Due to uncertainties in the modeling, amplitudes at maximum i.e. for $ell=1$ at 60 $mu$Hz can range from 3 to 6 mm s$^{-1}$.
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