Aspect-Based Sentiment Analysis (ABSA) is a fine-grained task in sentiment analysis, aiming to identify sentiment expressed towards specific aspects of an entity. This paper explores the use of Large Language Models (LLMs), specifically GPT-3.5-turbo and Llama-3-70B, for generating annotated data in Aspect-Based Sentiment Analysis (ABSA), aiming to address the scarcity of labelled datasets in the field. Two low-resource scenarios are considered, with 25 and 500 manually annotated examples available. In the 25-example scenario, adding synthetic examples generated through few-shot prompting resulted in F1 scores of 81.33 for Aspect Category Detection (ACD) and 71.71 for Aspect Category Sentiment Analysis (ACSA). For the 500-example scenario, synthetic data augmentation showed a notable gain only for the ACSA task, raising the F1 score from 84.54 to 86.70.