sefer continues where sefer Bereishit left off. And, at the end of Bereishit, the Israelites have already lived in Egypt for many years, Yaakov blessed his sons, and Yosef died. If so, how could the pasuk say that they are coming to Egypt now?
On a peshat level, this is no question. The sefer begins by reiterating that Yaakov came to Egypt with relatively few (12 sons, seventy souls), a count that occurred earlier in parshat Vayigash. Since the sefer is about the Exodus from Egypt, stylistically it makes sense to reiterate their entrance. Further, the stress is on how few their were (70 souls) in order to lead into the Israelites increasing abundantly, which prompts the Egyptian reaction. Thus, one can claim that there is no claim that the Israelites are entering Egypt now.
One can explain this question on a midrashic level, though -- and it is a midrashic question, raised in Midrash Rabba. The word הַבָּאִים is present tense - who are coming. Of course, Hebrew does not really have a present tense - just a neutral tense, and so the JPS translation is perfectly fine rendering it as "who came into Egypt." A midrash will take this at its most hyperliteral level, and thus can assume that it means they are coming now. Further, this sefer immediately follows Bereishit, and while saying that the Torah does not follow chronological order is acceptable, it is not the default. Thus, again operating hyperliterally, the pasuk seems to say that at this point in the narrative, the sons of Israel are entering Egypt.
Midrash Rabba answers that indeed, they are now, at this stage in the narrative, considered as if they are entering Egypt. Until this point, they felt no oppression, because of Yosef's influence. Only now does the oppression start, and thus their stay in Egypt can be considered to have begun.
Besides being a cute teretz, this midrash, like many a midrash, is based on a sensitivity to theme. Indeed, the account of the names and number of Yaakov's family is immediately followed by:
pasuk immediately preceding those of sefer Shemot, in Bereishit 50:26, is:
|כו וַיָּמָת יוֹסֵף, בֶּן-מֵאָה וָעֶשֶׂר שָׁנִים; וַיַּחַנְטוּ אֹתוֹ, וַיִּישֶׂם בָּאָרוֹן בְּמִצְרָיִם.||26 So Joseph died, being a hundred and ten years old. And they embalmed him, and he was put in a coffin in Egypt.|
While on the subject, note that the midrash is perfectly fine taking a genealogy and count which is described as הַבָּאִים מִצְרָיְמָה as one which occurs much later, at Yosef's death, taking the הַבָּאִים מִצְרָיְמָה somewhat figuratively as a result of taking other elements of pesukim hyper-literally. As I commented earlier on parshat Vayigash, there are many peshat reasons to take even the count in sefer Bereishit not of those physically entering Egypt at the time of initially entering Egypt, but rather of the Israelites at a later time, say Yaakov's death or Yosef's death. הַבָּאִים מִצְרָיְמָה would not refer to the act of entering Egypt but rather acts as an adjective, giving the count of the Israelites in the generation/approximate time period of the entrance to Egypt, as opposed to the Israelites who left Egypt, numbering 600,000. Thus, the conclusions of this midrash may well be true even on a peshat level.
(In addition to the evidence in the aforementioned post (on Vayigash) which implies that the count was not from the moment of entering Egypt but rather of some later point (and is a count of the generation which entered Egypt), I would add the following, which occurred to me last week. Ephraim and Menashe are part of the count of 70 (see Bereishit 46:27). Yaakov lived in Egypt for 17 years (see Bereishit 47:28). Yet when they are blessed, Ephraim and Menashe seem to be little children. They are called nearim (although Yosef too, one may argue, is called a naar at 17). The feel from the stroy is that they are much younger. The midrash (Rabba and Tanchuma) makes Menashe somewhat old at the time of the entrance into Egypt, for it is he who strikes Shimon, puts him in prison and in fetters. Add 17 years to this and he must be in his twenties. Peshat is probably that Ephraim and Menashe are fairly young when they receive Yaakov's blessings in parshat Vayechi, and thus the genealogical list should be of a later date than the entrance into Egypt.)