  In this analysis we apply a model-independent framework to test the flat
$\Lambda$CDM cosmology using simulated SNIa data from the upcoming Large
Synoptic Survey Telescope (LSST) and combined with simulated Dark Energy
Spectroscopic Instrument (DESI) five-years Baryon Acoustic Oscillations (BAO)
data. We adopt an iterative smoothing technique to reconstruct the expansion
history from SNIa data, which, when combined with BAO measurements, facilitates
a comprehensive test of the Universe's curvature and the nature of dark energy.
The analysis is conducted under three different mock true cosmologies: a flat
$\Lambda$CDM universe, a universe with a notable curvature ($\Omega_{k,0} =
0.1$), and one with dynamically evolving dark energy. Each cosmology
demonstrates different kinds and varying degrees of deviation from the standard
model predictions. We forecast that our reconstruction technique can constrain
cosmological parameters, such as the curvature ($\Omega_{k0}$) and $H_0
r_\mathrm{d}$, with a precision of approximately 0.52\% for $H_0 r_\mathrm{d}$
and between 0.032 to 0.037 for $\Omega_{k0}$, competitive with current cosmic
microwave background constraints, without assuming any form of dark energy.
