How to check machine learning accuracy without cross validation
Splitting your data is critical for evaluation. 
There is no way that you could train your model on 100% of the data and be able to get a correct evaluation accuracy unless you expand your dataset. I mean, you could change your train/test split, or try to optimize your model in other ways, but i guess the simple answer to your question would be no.
I have training sample X_train, and Y_train to train and X_estimated.
I got task to make my classificator learn as accurate as it can, and then predict vector of results over X_estimated to get close results to Y_estimated (which i have now, and I have to be as much precise as it can). If I split my training data to like 75/25 to train and test it, I can get accuracy using sklearn.metrics.accuracy_score and confusion matrix. But I am losing that 25% of samples, that would make my predictions more accurate. 
Is there any way, I could learn by using 100% of the data, and still be able to see accuracy score (or percentage), so I can predict it many times, and save best (%) result?
I am using random forest with 500 estimators, and usually get like 90% accuracy. I want to save best prediction vector as possible for my task, without splitting any data (not wasting anything), but still be able to calculate accuracy (so I can save best prediction vector) from multiple attempts (random forest always shows different results)
Thank you