This is the first time (that) I have been to the summer pala

the first time 不表示连词,只是第一次的意思.
连词一般指承接,转折的意思
如 and but or..
the first time, 这里的the是冠词, 强调这一次（time）,是第一次（first）.
带有宾语从句的复合句就是用连接词把一个主句和一个宾语从句连接在一起.连接词有：that(可省略),what, who, when, where, why, which, if, whether, how.
你这个句子里面,有两个主语,the first time, 和 I, 所以需要用that从句将句子连接起来.
但是that时常何以省略.
除非：
当主句谓语动词带有两个或两个以上宾语从句时,可以省略第一个that,其他不能省略.
I believe（that）you have done your best and that things will get best?
当it作形式宾语时
She made it clear that she had nothing to do with him．
当宾语从句前置时
That our team will win,I believe．
希望能帮到楼主