How to train RNN without a teacher?

I have a project that models evolution, especially since I don’t have the right answers for backpropagation. But I need the neural network to remember the past and understand sequences, RNN(GRU, LSTM) and Transformer would be suitable for this (they require many times more computing resources and a training sample), but I couldn’t even find Reinforcement Learning for them, let alone NEAT or GA, like MLP. Now I just don’t know what to do, maybe I need to take MLP and give tens of neurons of the input layer to memory, but I don’t think this solves the problem.