Timeliness is an emerging requirement for many Internet of Things (IoT) applications. In IoT networks, where a large-number of nodes are distributed, severe interference may incur during the transmission phase which causes age of information (AoI) degradation. It is therefore important to study the performance limit of AoI as well as how to achieve such limit. In this paper, we aim to optimize the AoI in random access Poisson networks. By taking into account the spatio-temporal interactions amongst the transmitters, an expression of the peak AoI is derived, based on explicit expressions of the optimal peak AoI and the corresponding optimal system parameters including the packet arrival rate and the channel access probability are further derived. It is shown that with a given packet arrival rate (resp. a given channel access probability), the optimal channel access probability (resp. the optimal packet arrival rate), is equal to one under a small node deployment density, and decrease monotonically as the spatial deployment density increases due to the severe interference caused by spatio-temproal coupling between transmitters. When joint tuning of the packet arrival rate and channel access probability is performed, the optimal channel access probability is always set to be one. Moreover, with the sole tuning of the channel access probability, it is found that the optimal peak AoI performance can be improved with a smaller packet arrival rate only when the node deployment density is high, which is contrast to the case of the sole tuning of the packet arrival rate, where a higher channel access probability always leads to better optimal peak AoI regardless of the node deployment density. In all the cases of optimal tuning of system parameters, the optimal peak AoI linearly grows with the node deployment density as opposed to an exponential growth with fixed system parameters.