Key feature fields need bigger embedding dimensionality, others need smaller. This demands automated dimension allocation. Existing approaches, such as pruning or Neural Architecture Search (NAS), require training a memory-intensive SuperNet that enumerates all possible dimension combinations, which is infeasible for large feature spaces. We propose DimGrow, a lightweight approach that eliminates the SuperNet requirement. Starting training model from one dimension per feature field, DimGrow can progressively expand/shrink dimensions via importance scoring. Dimensions grow only when their importance consistently exceed a threshold, ensuring memory efficiency. Experiments on three recommendation datasets verify the effectiveness of DimGrow while it reduces training memory compared to SuperNet-based methods.