In large-scale wireless networks, severe interference may incur that leads to the age of information (AoI) degradation. It is therefore important to study how to optimize the AoI performance. This paper focuses on the average AoI minimization in random access Poisson networks. By considering the spatiotemporal interactions amongst the transmitters, an expression of the average AoI is derived, based on which the optimal average AoI and the corresponding optimal packet arrival rate and channel access probability are further characterized. We further compare the average AoI optimization with the peak AoI optimization. The comparison reveals that the optimal channel access probability for the average AoI optimization and the peak AoI optimization are the same. Yet, the optimal packet arrival rate for the average AoI optimization is smaller than that for the peak AoI optimization. The gap enlarges when the node deployment density becomes small.