Shortly after the covid19 hit the world, she and other 11 students formed a group to provide/ providing food for those in need.

【1】Shortly after the covid19 hit the world, she and other 11 students formed a groupto provide food for those in need.

=To provide food for those in need, he and other 11 students formed a group shortly after the covid19 hit the world.

=In order to provide food for those in need,he and other 11 students formed a group shortly after the covid19 hit the world.

参考译文:为了给有需要的人提供食物，他和其他11名学生在新冠肺炎疫情爆发后不久成立了一个小组。

备注：以上填不定式“to provide”作目的状语成分。可以把不定式“to provide”或者“in order to provide”放在句首表示强调。不定式“to provide”作目的状语是用来修饰句子谓语的，即成立一个小组的目的是为了(做)什么。

【2】Shortly after the covid19 hit the world, she and other 11 students formed a group providing food for those in need.

=Shortly after the covid19 hit the world, she and other 11 students formed a group which provides food for those in need.

参考译文：新冠肺炎19疫情爆发后不久，她和其他11名学生组成了一个为有需要的人提供食物的小组。

备注：以上填现在分词“providing”作后置定语成分。可以改为对应的定语从句“which provides”。在分词“providing”作后置定语是用来修饰名词的，即用来说明或者描述该名词的属性，特点，性质以及功能和作用是什么。

最后总结：以上语法填空 填不定式“to provide”或者现在分词“providing”都是正确的，如果提问网友填了现在分词“providing”也是正确的。