AMoRE searches for the signature of neutrinoless double beta decay of \(^{100}\)Mo with a 100 kg sample of enriched \(^{100}\)Mo. Scintillating molybdate crystals coupled with a metallic magnetic calorimeter operate at milli-Kelvin temperatures to measure the energy of electrons emitted in the decay. As a demonstration of the full-scale AMoRE, we conducted AMoRE-I, a pre-experiment with 18 molybdate crystals, at the Yangyang Underground Laboratory for over two years. The exposure was 8.02 kg\(\cdot\)year (or 3.89 kg\(_{\mathrm{^{100}Mo}}\cdot\)year) and the total background rate near the Q-value was 0.025 \(\pm\) 0.002 counts/keV/kg/year. We observed no indication of \(0\nu\beta\beta\) decay and report a new lower limit of the half-life of \(^{100}\)Mo \(0\nu\beta\beta\) decay as \( T^{0\nu}_{1/2}>3.0\times10^{24}~\mathrm{years}\) at 90\% confidence level. The effective Majorana mass limit range is \(m_{\beta\beta}<\)(210--610) meV using nuclear matrix elements estimated in the framework of different models, including the recent shell model calculations.