  We propose an algorithm to recursively bootstrap $n$-point gluon and graviton
Mellin-Momentum amplitudes in (A)dS spacetime using only three-point amplitude.
We discover that gluon amplitudes are simply determined by factorization for
$n\geq 5$. The same principle applies to $n$-point graviton amplitudes, but
additional constraints such as flat space and soft limits are needed to fix
contact terms. Furthermore, we establish a mapping from $n$-point
Mellin-Momentum amplitudes to $n$-point cosmological correlators. We
efficiently compute explicit examples up to five points. This leads to the
first five-graviton amplitude in $AdS_{d+1}$.
