at first 作时间状语,句子的时态没有什么限制,根据语境可以是任何时态,例如:
Some of the space will at first be used for storage. 一些空间将首先用于贮藏(摘自《柯林斯英汉双解大词典》)(本句用了一般将来时)
I didn't like the job much at first. 起初我并不很喜欢这份工作(摘自《牛津词典》)(本句用了一般过去时)
She had liked him at first but soon lost interest. 最初她喜欢过他,但很快失去了兴趣(摘自《柯林斯英汉双解大词典》)(本句用了过去完成时)