Predicting time series, with few historical samples based on similar series
I'd suggest statistical forecasting techniques such as ARIMA or ES, but those models usually cannot generalize well across timeseries, so you'd need one for each timeseries

A good starter for using LSTM for forecasting is here - https://www.tensorflow.org/tutorials/structured_data/time_series. But if you don't have enough data, NNs would like result in poor test results.

For your case, I'd suggest you trying a regression approach- structuring your timeseries into a regression features format. After that you can use regression models from sklearn, starting with linear and moving to more complex ones. Because you have less data, you might want to explore less complex models first to prevent overfitting. For the features, for example, you could create lag features (what was the value of your signal two timestep back, what was the mean/std of the past 2 timesteps, what was the maximum in the last 6 timesteps and so on). Look up any kaggle competition on timeseries forecasting if you want to refer code or get specific ideas on feature extraction