Multi-omics data capture complex biomolecular interactions and provide insights into metabolism and disease. However, missing modalities hinder integrative analysis across heterogeneous omics. To address this, we present MOIRA (Multi-Omics Integration with Robustness to Absent modalities), an early integration method enabling robust learning from incomplete omics data via representation alignment and adaptive aggregation. MOIRA leverages all samples, including those with missing modalities, by projecting each omics dataset onto a shared embedding space where a learnable weighting mechanism fuses them. Evaluated on the Religious Order Study and Memory and Aging Project (ROSMAP) dataset for Alzheimer's Disease (AD), MOIRA outperformed existing approaches, and further ablation studies confirmed modality-wise contributions. Feature importance analysis revealed AD-related biomarkers consistent with prior literature, highlighting the biological relevance of our approach.