If you look at the bitcoin market in October in the past years, it can be understood that it was always positive, but no one can say whether this October will be positive or negative. But OP, if you have a desire and have enough opportunities to invest, you can invest in early October.
Bull-season is getting closer as days go by, but I think that the beginning of October will be bullish, but I don't think this month will be bullish or positive. Already Bitcoin has dropped to 58k. But if someone wants to invest now, I will definitely not say it is the ideal time because when the market is bullish, no big investment is ideal. The investment time is the bear season when we do not invest because of fear.
But as like me also wanna say if you want to investment on bitcoin and you have fund for that then you can make investment withe the DCA strategy which will cost low risk also.