There are valid mathematical reasons for this. Delta is derived from the Black-Scholes formula for pricing options and represents roughly how much the option behaves like the underlying stock. Generally, it would be a minimum of three months from the IPO date before options could be listed on any stock.
Liquidity refers to the availability of stock near the last sale price.
Sometimes that means that the stock is more volatile, but not always. It is possible, for example, to have a volatile stock that is very liquid, meaning that there are usually lots of stock shares to buy or sell at prices near the last sale. In that case, the options' bid-ask would most likely be narrow. When the market in an option is narrow, it may mean that shares of the underlying stock can either be bought or sold in quantity near the last sale price or the option itself has a lot of buyers and sellers near the last sale price of the option. Usually if an option is liquid, the underlying stock is also liquid.