You can
open a bank card and online banking first, and open a fund trading account. Go to online banking when you get home. If you want to buy a fund from that fund company, you can open a fund account under that fund company, and then you can apply for or subscribe.
Buying a newly issued fund is called subscription, and it's all one yuan each, with a closed period, during which you can't redeem it.
Buying a fund that has been issued is just subscription, and the price depends on the market of the day. There is no closure period.