for the first time作为介词词组，意为第一次，在句中一般用作状语，修饰动词；the first time意为初次、第一次…的时候，后面可接that/when引导的定语从句。
for the first time在句中只能作状语，he first time可作表语和主语。
I went there for the first time. 状语
The first time i saw the film was last month. 主语
It is the first time I drink wine. 表语
1、the first time
主要有以下2个用法：
(1)作为名词词组，作句子主语和表语，后面御昌培接that定语从句。
This is the first time that she has come here.
这是她第一次来这里
This is the first time that she has experienced disappointment.
这是她第一次感受到失望。
(2)作为连词，引导时间状语从句
Mary was a shy girl the first time I met her.
我第一次玛丽时是一个害羞女孩。
2、for the first time
是个介词短语，意为“第一次，首次，初次”，一般用作状语，修饰谓语动词，可以放在句首，可以放在句末。
For the first time the government's actually put some money up front.
政府居然预付了一笔钱，这可是有史以来第一次。
For the first time in many years, I got carded.
这么多年来，头一回有人要我出示身份证。
Several of these rhododendrons will flower this year for the first time.
这些杜鹃花有些将在今年首度开花。
There is no feeling on earth like winning for the first time.
初尝胜利滋味镇唯的感觉真是无可比拟。
first介绍
first为序数词或者副词，表示最早的，最先的，第一位的，起初，最早，最先，先，作定语或者状语。
She lost 16 pounds in the first month of her diet.
她节食的头一个月就减掉了16磅。
When he first came home he wouldn't say anything about what he'd been doing.
刚回到家时，他只字不提自己一直在做什么。
I do not remember who spoke first, but we all expressed the same opinion.
我不记得是谁最先发言的，但我们全都表迅伍达了相同的看法。
First, tell me what you think of my products.
先谈谈你觉得我的产品怎么样吧。
以上内容参考：first(英语单词) - 百度百科
