我谈一点粗浅的看法，不一定对。仅供参考，同时希望其他老师也积极发表看法。
这个句子要表达的意思是：吉姆的作文就是这样开始的。
这里的 so 所表达的意思是 like this 或 like that。个人认为应改为：Jim's composition begins (just) like this.
在《牛津英语用法指南》（2010 年 4 月版 P. 835-836）中对于 so 表示 like this / that 的意义时有如下说明：
1. 在 seem, appear 等后面
在少数情况下，so 可以用在正式文体中，表示“像这样/那样”，“以这种 / 那种方式”。例如，这种情况出现在 seem,appear, remain, more 和 less后面。
Will the business make a loss this year? ~It appears so. 今年生意会亏本吗？~ 看来是这样。
The weather is stormy, and will remain so over the weekend. 天气多暴风雨，而且将持续到周末。
She was always nervous, and after her accident she became even more so. 她总是紧张不安，自发生事故以来，她更是如此。
I read the front page very carefully, and the rest of the paper less so. 我非常仔细地阅读了报纸的头版，对其他版面就不那么仔细了。
2. 不用在其他情况
在其他情况下，so 通常不用作副词来表示“像这样/那样”，“以这种 / 那种方式”的意思。
Look － so hold it up in the air like this. 瞧—— 像这样把它举在空中。（不能说:... hold it up in the air so.）
When he laughs like that I want to scream. 他那样笑的时候，我真想尖叫起来。（不能说：When he laughs so ...）
I don't think we should do it in that way. 我认为我们不该以那种方式做事。（不能说：... do it so.）
He says he is ill and he looks it. 他说他病了，看起来是真病了。（不能说：... he looks so.）

【Thus began the】：

1.Thusbegan the Peace Movement which continued through the remainder of the year withmarches and hymnsinging rallies and which led to the award in 1977 of the NobelPeace Prize to Mairead Corrigan and her co-founder, Mrs. Betty Williams.

2.The Elves landed and thus began the battleof the waves.

3.Thus began the great age of Elfscholarship.

4.Jennings thus began The Law and theConstitution with an examination of the functions of government and, in anapproach reflecting the influence of sociological positivism, commenced with anoutline of the growing interdependence of society founded in the increasingdivision of labour.

5.Thus began the French phase of the Vietnamconflict which was to last eight years.

6.Thus began the last chapter of a case thathad started as a simple bank robbery, then extended into one of murder andfraud, and drugs.