experience/ability in teaching and securing external funds for getting professorship
Your question is based on a few statements which I believe are misunderstanding or over-generalisations.


  Postdoc fellowships are only the external funds I (as an early-career postdoc) can secure.


A fellowship is definitely the most significant external funding a postdoc can typically secure. If you manage to get such a fellowship, you most likely will tick a "funding" box on your tenure-track application in most places. However, this is not the only type of funding postdocs can go for. You can bid for funds to attend conferences, you can often bid for smaller pots of money to organise workshops, conferences, and share knowledge in science fairs, exhibitions,  outreach events. You can also engage in knowledge transfer and get funding from industries or other end-users of your research. And of course you can collaborate with established professors and get your name as a Co-Investigator or sometimes second PI on the grants they submit.


  Teaching opportunity is also limited.


This is true, in principle: postdocs' main aim is to do research and they normally are not expected to teach more than 20% of load. However, although there is a time restriction, it does not limit one's ability to engage fully with various ways teaching is or can be done. If you only do marking for 20% of your time, that does not tick the "teaching" box so well. But if you also conduct tutorials, occasionally deliver a lecture or two, design a (part of) the assessment, contribute a bit to designing the teaching materials, it presents you much better as a well-rounded person who can be put in front of students and trusted with a course. If you also have or start work towards a recognised teaching qualification - even better.